South Vietnam was helped by US. Even when the US was gone, they had a 1 million army.
So why did they lose?
Even without US support, South Vietnam had about the same manpower, higher technology, and was more industrialized. Why did they lose?
First of all, to clarify what you asked in the subject, the US didn't "lose" the Vietnam war militarily. The Tet Offensive was basically a disaster for the Viet Cong and the forces of North Vietnam – they didn't achieve their intended strategic objective (popular uprising in the south) and suffered major losses.
However, the US populace lost the will to fight in that war - as noted by others, they started viewing the war as "not worth fighting" (rightly or wrongly). The USA being a democratic republic, fighting a war that the majority of the people oppose and which has no geopolitical significance is not something those in power can realistically bother with.
North Vietnam was also being heavily militarily helped by the USSR (not sure about China), and that did NOT stop when the USA went home
There was a significant portion of populace in South Vietnam that wanted the North to win - they weren't "foreign" invaders, and the poorest parts of society are generally a lot less resistant to the idea of an ostensibly "we are for the poor" political forces taking over.
Moreover, your quip at the end - while not exactly correct - has two grains of truth.
First, of all, dictatorships and totalitarian countries are a a lot less likely to care about significantly higher losses. Both from intrinsically lower value on human life, AND from far lower effect of losses on country's and military's morale.
Second, people with less to lose and less to live for are a lot more willing to risk death for some sort of cause on average.
Up until Vietnam, the US had been training their military to fight a "conventional" war, more along the lines of what they fought in each of the World Wars. In Vietnam, the fighting was very "unconventional". In each WW, they could easily identify the enemy because they wore different uniforms and spoke a different language. In Vietnam, the enemy spoke a different language, but it was the same language as the military they were supporting. Furthermore, their enemy did not customarily wear uniforms. It was easy for them to melt into the surrounding populace without being clearly identifiable.
Another factor was the guerilla warfare. Much of the fighting in Vietnam involved night raids by the North, as well as surprise ambushes and quick assaults that melted away into nothing. What I mean by that is that the enemy would seem to disappear because they were so adept at blending into the landscape and they also made extensive use of tunnels to allow them to move troops and supplies. The US was ill equipped and poorly trained in how to fight a guerilla war.
When you look back in the history of the US, you could ask the same question about how the US was able to defeat the British during the Revolutionary war. The answer is basically the same. The US did not fight a "conventional" war, they were better able to make use of their surroundings and the terrain, and they fought a number of smaller skirmishes rather than trying to launch a full out attack against superior forces.
In both scenarios, there was definitely an advantage to fighting on your own soil. Your supplies are more easily replenished and it is easier to muster support from the rest of the country. In both cases, the home team just had to outlast the willingness and desire of the "invaders".
The main reason was that the people just supported the North. The reasons may vary, but the South were considered a force fighting for the interests of the invaders and the North were simply liberators.
One of the previous answers notes that totalitarian governments can sustain higher losses. This does not do anything with the reality of Vietnam. How can you imagine a "totalitarian government" in a forest? In civil war usually wins the side which is more supported by the people, because people can easily defect and switch the sides, and no "totalitarian government" can do anything with it. The people in the North just loved their motherland while those from South loved their money.
In my opinion, I think the only reason US+South Vietnam lost the war is due to the willingness of Southern people in the war. Vietnamese people have a long tradition of nationalism. They don't accept any invasion from outsiders. North Vietnam took advantage of this. They conducted propaganda to show that US was invading Vietnam and Vietnamese people had the duty to fight back.
In 1996, the North Vietnamese defense minister published an article in the Wall St. Journal about the moment when he felt that North Vietnam had won the war. It was when "Hanoi" Jane Fonda went to the North Vietnamese capital in 1972 to express her "solidarity" with them, returned home, and wasn't severely punished. Then the North Vietnamese felt that she basically spoke for the American people (who didn't want war). After the Americans finished pulling out later that year, the North Vietnamese redoubled their efforts (against the South Vietnamese only), and won.
We lost the war in Vietnam because the American public no longer supported it. You can speculate on any number of reasons for this. People stopped believing the Domino Theory. Americans did not feel threatened by the Vietcong or North Vietnam.
It was part of the larger Cold War, but American public could not tolerate the death toll of Americans for purely ideological reasons. The South Vietnamese government was riddled with corruption with little real support from the South Vietnamese people. After years of claiming that they were winning the war, the Tet Offensive blew a huge hole in the American military's credibility. Even if Tet was a military defeat for the North Vietnamese, the American public did not see it that way.
In the end, the Vietnamese were far more willing to die for their country than we were willing to keep on killing them. They were, and are, a tremendously resilient people. Maybe it is better to speculate on why the Vietnamese communists won rather than why Americans lost.
Shortly after the end of the Vietnam War, the Vietnamese invaded Cambodia and stopped the genocidal slaughter there. They were really spurred on by the Soviets who didn't want the Chinese-supported Pol Pot regime to win. But it was also the right thing to do, and no one else would do it, including America.
The short answer is that it was impossible for South Vietnam to win. The single biggest strategic issue was the People's Republic of China.
Successive American governments feared that if they invaded North Vietnam this would provoke Chinese intervention, just like in the Korean War. There was also a fear that this could escalate into war with the USSR.
In late 1964 the People's Republic of China tested their first atomic bomb: 596. By mid 1965 they had developed airborne delivery, and in 1966 the PRC was able to equip medium ranged missiles with nuclear warheads. The evidence is that Mao was not only willing to intervene in Vietnam, but was also preparing for it.. A combination of Maoist enthusiasm for intervention, and China's newfound atomic weapons, represented an exceptionally dangerous risk.
Consequently America was unable to defeat the regime in Hanoi, and so long as North Vietnam existed they would always work to overthrow the regime in Saigon. Officially America framed the war in the context of anti-Communism, but this was a fundamental error.
When Ho Chi Minh studied in Moscow his peers remarked that he was a nationalist first and a communist second. That was typical of the North Vietnamese mentality. It's understandable given history. Vietnam had been occupied by the French and Japanese, and it was believed that Saigon was just another puppet regime created by a colonial power.
South Vietnam's behaviour justified arguments against it. From the start the regime was plagued with blatant vote rigging, corruption, and institutional discrimination. The government was run by Vietnamese Catholics, who represented little more than 10% of South Vietnam's population. Promotion in the civil service and armed forces was often based on nepotism and religion; not merit. The South Vietnamese elite repeatedly provoked the vast majority of their own people, who were rural Buddhists.
All this led to the Buddhist Crisis, when peaceful protesters were shot dead by South Vietnamese soldiers. In response monks began to protest discrimination by burning themselves alive. This situation embarrassed America, and seemed to prove that the government in Saigon was indeed just another oppressive form of colonial minority rule.
America escalated their involvement in Vietnam out of fear. JFK and LBJ felt trapped by hysterical anti-Communism at home. At this point it was widely believed that America was losing the Cold War. Eastern Europe and China had fallen, and the Bay of Pigs had been a disaster.
In 1962 JFK remarked:
"If I tried to pull out completely now from Vietnam, we would have another Red scare on our hands."
In 1963 he said privately:
"We don't have a prayer of staying in Vietnam.... But I can't give up a piece of territory like that to the Communists and get the American people to reelect me."
As the war escalated so too did the body count. This was a way the White House attempted to prove they were winning. The argument went that there was a tipping point, after which North Vietnam could not replenish its losses and victory would be inevitable.
But this never happened. Instead civilian casualties became routine. Dead civilians were often tallied as Viet Cong, and American soldiers were sometimes told to assume anyone running away was a hostile target. There were many massacres by American soldiers. Most notably My Lai, where over 340 people, overwhelmingly women and children, were raped and murdered. More would have died had an American helicopter pilot not tried to stop it by landing between the Americans and the fleeing villagers. These incidents further eroded American credibility. When the war ended America had killed up to two million civilians.
By 1970 American morale was in free fall. War exhaustion was high. For years the American military had claimed it could win. It just required twenty thousand more soldiers... two hundred thousand more soldiers... another two hundred thousand soldiers. This pattern of repeated boasts and failures was becoming evident to most.
Even though the North's Tet Offensive in 1968 was a tactical failure with thousands dead on both sides, it shocked and unnerved the establishment. They were worried by Hanoi's ability to conduct such a massive operation so late in the war, and to still be able to keep going after it had failed.
Public opposition to the war and draft was common. Many Americans were angry that they and their friends and family were expected to die for an unwinnable war. There had been a spike in "fragging". American soldiers tried to kill their own officers, usually with hand grenades. There were over 360 such events recorded in 1971 alone, and that year the Armed Forces Journal declared:
“morale, discipline and battleworthiness of the U.S. Armed Forces are, with a few salient exceptions, lower and worse than at any time in this century and possibly in the history of the United States.”
Ultimately South Vietnam fell because victory was strategically impossible given the threat of Chinese intervention.
South Vietnam repeatedly undermined itself with institutional corruption and discrimination. It failed to become a viable alternative to the North.
Consequently North Vietnam successfully presented itself as a means for the Vietnamese people to achieve national liberation.
American support for Saigon escalated due to the politics of fear and saving face, instead of a rational analysis of whether they could win or not.
The American presidency and military regularly boasted victory would happen sooner rather than later, and yet the war became the longest in US history. This led to the collapse of public and congressional support.
The threat of global communism was greatly exaggerated, as relations between communist states quickly deteriorated. By 1961 the PRC and USSR were publicly denouncing each other, and the PRC and North Vietnam regarded each other with contempt. Global communism would win the war, but it couldn't survive the peace.
The only reason the south lost is because in April 30th 1975, they were already in sai gon fighting there last battle but they surrender because they did not want another event like Hue they still have the other marine regiment they could just call the marines that's still left out there back and take a last stand in sai gon but by that time if they do that then the vc had fire in to the city, killing civilians so that's why they surrendered it's because they did not want any more civilians to die