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?