Even a factory machine built string should last a lot longer than that. You didn't say where the string broke. That is very important information. You need to know if it's possible a bur on a cam cut it. If it broke where the release attaches, the problem could be with your release. In fact, if it broke where the peep attaches, it's possible it was installed incorrectly, or a strand broke on installation.

No sense in replacing a string, until you know the new string won't break because of problem unrelated to the contruction of the string.