Probably about as long as the zipper on your jeans...
But seriously, if no moisture were able to get into the powder, they would probably last indefinitely. But it's nearly impossible to keep moisture out unless the shells were sealed with wax, both at the primer and at the top wad as well.
I bought a very old box of .22 WRF cartridges that looked nearly new... the cardboard looked entirely new, as did the bullets (no signs of oxidation on the lead bullets) but when I went to shoot them not a one of the fifty would fire. Somehow the primer substance failed.
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