Modern military ammo actually has a somewhat shorter lifespan than World War II era military ammo. Back in World War the chemicals used in the primers were corrosive to the bore if the weapon was not cleaned after firing.
After WWII most militaries (including the U.S.) switched to non-corrosive primers (different chemical mix) so that bore corrosion would not be as much of an issue. The downside was the non corrosive primers don't have the same incredibly long lifespan as the corrosive primers.
For example, I've fired ammo from WWII fairly often. If it was stored well, in a stable temperature environment, with low humidity, it works great. However, I've also fired some that was obviously stored poorly because I've had multiple misfires and hangfires with certain batches.
For modern ammo, how long do you need it to be useable for the story? The longer you need, the more the ammo should have been stored in ideal conditions. What you'd want is military ammo, stored in sealed containers, in at least a case lot size. You'd want the ammo to still be in storing/shipping containers of the kind designed for longer term storage, not already broken up into smaller units for distribution, as that means it would have been taken out of the nitrogen sealed containers.
As to duration, anything under about 70 years is definitely possible as I've fired non corrosive ammo made right at the end of WWII.
As to over 100 years, I'd say it's plausible, assumed good storage conditions. Anything further out from that gets iffy. If you want to add some insurance to help "suspension of disbelief" you could have the characters experience some problems with ammo misfiring from time to time.