"Not willing to fight hard enough" Hard ENOUGH to do what? To win? I guess by definition you could say that if they are not willing to fight hard enough to win, then they will lose.
While there have certainly been cases in recent times where one country has invaded another and then been defeated or forced to withdraw,
I think the answer to your question is pretty clearly that it IS possible, because there are several instances where it has happened.
In 1968, the Soviet Union invaded Czechoslovakia and subjugated the country. They did not leave until the fall of the Soviet Union in 1989. Arguably that's not a good counter-example as the Soviets were ultimately forced out of all the countries they occupied, though the exact circumstances are complex.
North Vietnam invaded South Vietnam and conquered the country in 1975. They still control it. I think this is a clear counter-example.
In 1983 the U.S. invaded Grenada and installed a friendly government. The U.S. didn't conquer the country in the sense of annexing the territory, but the U.S.-friendly government is still there.
The case in Iraq is pretty ambiguous. The U.S. clearly defeated the Iraqi military, took over the country, and installed a friendly government. But then a new regime came to power in the U.S. that had little interest in retaining control, and began a voluntary withdrawal. Partly this was because of resistance, but mostly because they just didn't have any desire to retain control of the country. Iraq was then invaded by an outside power, ISIS. I say "outside" because they originally came from Syria. ISIS has support from some Iraqis, but I think it's fair to say that a majority of Iraqis do not support them. It's not at all clear how this will end. If ISIS ends up in control, that would be a counter-example.
In Afghanistan, the U.S. goal was to destroy the Taliban. It was never to conquer the country and make it a 51st state. So the U.S. achieved its goal and is leaving. That's not really a test of your thesis.