I agree with you, but I can store StarSan in a growler for months and it's fine. I do that with Iodophor and I get something that at least looks like mold.
Is it sealed? Once diluted, the iodine in an iodophor is able to sublimate, reducing its effectiveness pretty quickly. That would also apply to a relatively small amount of an iodophor in a sealed container with a lot of headspace.
When in doubt, a quick visual check should tell you what's what. If the solution is no longer yellow-orange, the free iodine content is too low to be effective.
I store iodophors in an airtight container for months, reusing them until they pick up particulates or lose their color. No problems yet, touch wood.