It depends what kind of sleeping pills, I would imagine. Can’t you just make up a brand of hypnotic, like Stephen King did with the narcotic pain killer Novril in Misery that suits the purpose of the story?
Given the complexity of modern pharmaceuticals a reduction of potency is not the only possible change to anticipate if you use drugs beyond their safe storage period. An increase in potency , or an entirely unrelated effect is possible as well.