Are you sure the strands weren't broken as a result of the peep sight itself or possibly the result of the installation of the peep? Being careful when burning the ends of the peep serving is a must. Even a small part of a string strand melted can result in broken strands after only a short period of shooting. On the other hand, if there is a sharp edge to the peep then that can cut the strands relatively quickly.

I can typically get at least 12 months of solid shooting out of my bows before a string change is warranted and not for separated strands.