I have a Martin Jaguar that I have had the same problem with since I purchesed it. The peep sight almost always twistes to the right after every shoot. sometimes to the piont that I have problems getting a good sight picture. I have replaced the string twice and have had two bow shops scraching they're heads on how to address the problem.
I'm using a Zero Peep with rubber tubing.
I would change to a new peep like a tri slot or shurz-a-peep if I thought it wouldnt twist on me during the hunt.