Ehhh. I think it's more: they quickly stop optimizing drivers for the old cards.
It's not so much about completely dropping support so much as older cards don't really see any performance gains (maybe even small performance drops) with new drivers. Whereas drivers will often state that they provide X% fps boost [in such and such games] for cards from the latest gen.this is common for both AMD and nvidia. in fact if you look at history it is AMD that is much faster drop support than nvidia. it happen with HD4k vs GTX200, HD5k/6k vs GTX400/500.
It's not so much about completely dropping support so much as older cards don't really see any performance gains (maybe even small performance drops) with new drivers. Whereas drivers will often state that they provide X% fps boost [in such and such games] for cards from the latest gen.