There is zero chance that potassium iodide goes bad after two years. I guess it's one of those bizarre things where all "medications" are required to have expiration dates.
Most of what is known about drug expiration dates comes from a study conducted by the Food and Drug Administration at the request of the military. With a large and expensive stockpile of drugs, the military faced tossing out and replacing its drugs every few years. What they found from the study is 90% of more than 100 drugs, both prescription and over-the-counter, were perfectly good to use even 15 years after the expiration date.
So, the expiration date doesn't really indicate a point at which the medication is no longer effective or has become unsafe to use. Medical authorities state if expired medicine is safe to take, even those that expired years ago. A rare exception to this may be tetracycline, but the report on this is controversial among researchers. It's true the effectiveness of a drug may decrease over time, but much of the original potency still remains even a decade after the expiration date. Excluding nitroglycerin, insulin, and liquid antibiotics, most medications are as long-lasting as the ones tested by the military. Placing a medication in a cool place, such as a refrigerator, will help a drug remain potent for many years.