I have trouble keeping cheese too, but the cheese I've most often bought must be cheddar. I guess either very hard Italian cheeses or cheeses immersed in oil are the only ones really to keep as "larder" items.
Larder is a good designation. I was thinking that I really don 't think of Parmesan as "cheese" but as a staple like butter, eggs, onions.,, Altho the good stuff is delicious enough on its own.
FWIW, my Genovese in-laws never popped for real Parmesan Reggiano but rather for "dry jack". Perhaps the latter is somewhat regional.