That depends on a lot of factors, so there's no one-size-fits-all answer.
For truly long-term, pro-level storage you want to look into slants and glycol (basically food-grade antifreeze). Those can last years.
I've not tried to store plates for very long at all (never used them to store a strain, only for transfers or cleaning up a print) so I can't speak to how long one might last. In any case it will last longer if stored in a dedicated refrigerator that you don't put any food in (a bar/dorm fridge works great for cleanly storing prints, plates, and syringes).