[quote=@Pepperm1nts]
[@Dinh AaronMk] 

That comparison to Vietnam would be valid if Vietnam had been invading the US, but that's not what happened. The American people grew tired of fighting a costly war overseas, because at the end of the day no one cared as much about Vietnam or communists if it meant losing thousands upon thousands of American lives on some foreign land.

The situation with the Turks here is way different. They were fighting off an invasion. And because they believed Anatolia to be their land, they should have fought harder for it. The heavy cost means a lot less when you are fighting for your own home. I think the Vietnam example you brought up is a bit silly in this context but if we're really going to use it, then the Turks fit the role of the North Vietnamese more than they fit the role of the US, since they were the ones being invaded. Armenia would be the one with the role of the invader. The problem then becomes that, since they both believe the land to be theirs, there is no "the cost is too high to prolong this war in foreign land". They would both want to fight hard for what they believe is theirs.
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It's only their home if they live there though. If the communities in Armenia are mostly Armenian then Armenia is only abstractly Turkish. The loss of Armenia might rub on Turkish pride, but it doesn't mean the Turks as a people or culture were threatened with subjugation or extinction. If the danger is abstract than the population will much more easily lose the will to fight. At some point, "The cost is too high to prolong this war in foreign land" does happen.

I mentioned Algeria earlier. I think Algeria is the closest equivalent there is. France identified heavily with their colony in Algeria, to the point that it was a eventually made a fully integrated member of France rather than a colonial second-fiddle, but they did eventually get forced to leave by native resistance. And France was not a collapsing Empire at the time.