If that thing is fraying off sometime before you get to the end of the stroke you most likely have something abraiding it .It could be a burr on the starter drum,a screw on the drum,rough rope guide bushing .
Not pulling to the end of stroke, and no rough spots but I'll have to take a super close look to verify the smoothness.
One theory I had was that making the rope too long was leaving the rope spooled to high or far out on the drum thus exposing it to wear from spinning parts.