My understanding of the statute of limitations in the US is that the "clock" on charges is stopped while you are out of the jurisdiction under which you've been charged. Technically that's true even across state lines, so if I broke a law in Alaska tomorrow and was charged for that crime after I'd left, and then visited Alaska again 20 years from now they could arrest me and make me face trial even if the statute of limitations on that crime would otherwise have long expired. Probably if the crime was so minor they wouldn't bother extraditing me they wouldn't bother arresting me when I returned but you never know.
Since Iran isn't going to extradite one of their citizens to the US - especially if he was working for the government - over this, the clock will remain forever stopped. He'd have to visit a country that had an extradition treaty with the US to have any worry though. Technically that could be Iran if someday relations got better, but in that case I imagine such cases would be dropped by mutual agreement.