In current times is it impossible to win a war if the people of invaded country are determined not to lose?

"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.

can an invader country only win the war if and only if the people of this invaded country want to lose it?

This doesn't make much sense, was there ever a war where someone wanted to lose? Did Nazi Germany want to lose WW2? No

It's still possible for an invaded people to lose if the odds are TOO overwhelming. One example was the so-called "battle" of the Warsaw Ghetto in 1943, where there were only 70,000 Jewish residents, armed with only a few hundred rifles, against crack German police and army units.

But the thrust of the question is, have modern times made it possible to mobilize the civilian population in such a way so that even if one army is decidedly smaller/weaker than the other, can the civilian population supporting the weaker army prevent a defeat. The lesson of Vietnam was yes. That is, the Americans had to defeat not only the regular Vietnamese forces, which they basically did, but also the North Vietnam civilian population, which was a much harder task.

Going back to World War II, the Germans failed to capture Stalingrad, because they had to fight not only the defending Soviet 62nd army, but in also the civilian population, which provided food, information, militia, and "replacements" to the Soviet army.

No. The USA had won the wars in Afghanistan and Iraq in any military sense. Their problems there are that they cannot keep the countries secure, safe and politically stable.

This is much different from Vietnam where they were opposed by a regular army, supplied from abroad and did not control the whole territory.

But indeed if an occupying army is very sensitive to casualties, a sparse insurgency and instability can force it leave.