Is it unfair to regrade prior work after detecting cheating?

I teach various undergraduate courses. I make the cheating policies clear on the first day of lectures, check the student's understanding of this with an on-line quiz, and remind students of the policy almost weekly in class. I try hard to detect cheating, but cannot catch everyone.

Sometimes I discover cheating mid-way through the semester. For example, I caught some students submitting duplicate assignments. After making the discovery, I looked back to past work that they submitted to the course Web site, and found the students sent identical papers for all past assignments, but I already awarded them A's.

Is it unfair of me to go back and regrade prior assignments when students cheated?

Looking over previous assignments after detecting cheating is perfectly reasonable. In fact, I'd advise that you should do it if you can.

Revising previous judgment calls about the quality of a student's work could be unfair, or at least extremely upsetting to the student. For example, it wouldn't be reasonable to say "Remember that paper I gave you an A- on? After thinking about it a little more, I've decided that I was too generous and your work deserved a B+ instead, so I'm changing your grade."

However, looking for evidence of cheating is different from reconsidering your grading standards. You aren't changing your opinion of the grade the work would deserve if it was properly done. Instead, you are trying to figure out whether it was in fact properly done. If not, then the student never earned the grade in the first place and has no cause to complain about unfairness.

In other words, there's no statute of limitations for cheating. Just because a grade has already been assigned, it doesn't mean you can't be found guilty of cheating, in which case the previous grade becomes irrelevant.