Depending on the type of string, it might just not be a particularly durable string or you might have gone past the recommended tension for the string you're using. The other possibility is that your stringer isn't doing a particularly good job.
All strings will fray over time at the intersections from rubbing against each other during hitting... some sooner than others depending on the jacket material. When that happens you'll start to lose repulsion and will need to restring.
I agree with Visor. No matter the tension or control of the player strings eventually fray due to friction. More so if you slice and dice a lot as it pressures the strings to move side to side more.
It's usually a sign that your strings are nearing its end of days. I'm talking about tiny wisps or some slight degradation in the string (usually around where they cross over each other) and not huge strands fraying off. If that's the case, I think you're getting some bum strings.