Considering this seriously for a moment, I would say it may depend on whether the poison is a liquid (which through dehydration could become more potent) vs other forms of poison which might see a reduction in potency. However, I don’t think any of them would deteriorate enough to lose their power and I certainly wouldn’t be willing to test my theories on myself.
I think the expression is "turn into a pumpkin" (obviously a reference to Cinderella's carriage magically turning back into a pumpkin at midnight) as if it's an all or nothing proposition. The physical properties of something don't just magically go bad as soon as a time or date is reached.
A lot of toxins are still virtually as potent as they were when first packaged. They're actually quite stable, but industry standard is to include an expiration date for many products.