It used to be that with the old tape on diapers with the actual tape the diapers would go bad because the tapes would lose their stickiness and the plastic backing would deteriorate.
But with the new cloth backed disposables with Velcro tabs they seem to last longer than the plastic backed diapers.
I would say that disposable diapers today should be good for at least 8 or more years in storage before they might go bad.