Constantinople was the focal point for the Fourth Crusade. The Christians lost and Constantinople went to the Ottoman Empire. Then, the European Christians became stronger and went about colonizing the rest of the world. In the meantime, the Ottoman Empire grew weaker. Yet, despite the Europeans' territorial ambitions as colonists, why didn't they try taking back Constantinople? The Ottomans have weakened, so it shouldn't be too difficult. Constantinople is present-day Istanbul.
Lemme have a go at this.
Its rather ironic that you bring up the Fourth Crusade as it is quite probably the reason Constantinople was lost to Christianity in the first place. Taking place in 1204-5 it was supposed to go to Egypt to fight there the Ayudid sultan who controlled the Holy Land but through a disastrous chain of events it got sidetracked into fighting and destroying the Byzantine Empire which was actually the main bulwark of Christendom in the east. The Latin Empire of Constantinople which replaced it for a brief 50 years was stillborn and the restored Byzantine Empire was at best a pale shadow of its former self. It was into this power vacuum, created by the crusaders' wanton destruction of the Byzantine Empire that the Ottomans stepped.
From about 1400 the Ottomans were in ascendant, constantly pushing back the Christian powers, taking the Balkan countries, twice besieging Vienna and conquering all of Venice's maritime possessions. (Venice was basically fighting them on her own for a few decades before being broken). They also had some setbacks (Vienna, Malta 1565, Lepanto 1571) and eventually a sort of stalemate ensued. During this time reconquering Constantinople was perhaps desirable to the Europeans but an absolute impossibility - they were barely holding to their own territory (and some, like Venice and the Balkan kingdoms lost it).
From the early 18 the century a new player arose - Russia. Starting with Peter the Great's relatively timid and unsuccessful campaigns against the Turks, Russia for 200 years had been putting increasing pressure on the Ottomans. At some point taking Constantinople became a major goal of Russian policy (Catherine the Great had her yonger grandson named Constantine as a heavy hint that she wished to have the boy one day seated on the throne of Constantinople). This coincided with two important developments (1) The constant and palpable decline in Ottoman power (2) The cooling of religious fervour both in Europe and Turkey.
During the second half of the 19th century Britain and to a smaller extent France were indeed propping up the Ottoman Empire (the proverbial "sick man of Europe") out of fear that Russia would seize the major part of its lands and dominate the Levant. So in a sense the Ottomans were now protected by their own weakness.
There was no "good" time for Europeans to take back Constantinople. As late as 1683, the Ottomans had the upper hand, besieging Vienna. Up to that point, Europe was more concerned about defending itself than about rolling back Ottoman power.
In the eighteenth and nineteenth centuries, the one European power that might have been able to take back Constantinople was Russia. But by that time, most of "Europe" feared Russia more than the Ottoman Empire. The Crimean War (1854) was fought by Britain, France and Piedmont to DEFEND Constantinople (against Russia).
The "Europeans" (British Empire) DID try to take back Constantinople with the Gallipoli campaign in World War I. It was a failure.
The Christian recapturing-(or "reconquest") of Constantinople has remained a dream for Greek Christians since 1453. The English and the French had strategic interests, though were less romantic when compared with the Greeks. For the Russians, it was perhaps a bit of both. Russians, like the Greeks, are both Eastern rite Christians and Constantinople, was (almost like) a Jerusalem by the Bosporus. However, Russians, like the English and French, also had a sizable empire and Constantinople, was a strategic prize, due to its enviable proximity to various seas and continents.
The attempt to recapture Constantinople has been tried by various Christian Powers over the last 100-200 years and all efforts failed. Even with the defeat of the Ottomans in World War I, as well as the subsequent dissolution of their centuries old Empire a few years later, as well as with the relocation of their Capital to the Central interior city of Ankara, the statistical and strategic Power and presence of the Turkish Muslims in this historic City has existed for hundreds of years and continues to remain strengthened.
You are forgetting that one of the small E. Euro countries near Constantinople did retake it for several years after WW1.
The crux of the matter is, European peoples have no ability to act as a social group, too individual. This allowed a much weaker, more backward Turkey to retake the city in the 1920s.
A more recent Turkish conquest was taking half of Cyprus after its independence from Britain in the 1970s. The Turks were so inept, the local Cypriot farmers continued to hold half the island, but again no response from Europe.
Currently, the Turks give millions of immigrants and Muslim financial aid to Islamizise the whole Continent, again no response from Europe, nay each country tries its best to funnel the immigrants on trains to Germany or Sweden.
Ottoman Empire allied themselves with Britain and France. They fought wars with Russian Empire and Greece, but were supported by the British and French forces. This way they won the Crimean war. Later they allied themselves with Germany in WWI. Despite the defeat of the Ottomans, Russia could not claim Constantinople because was excluded from the post-war negotiations by the British and the French.