Here is where the worn part sits in the clip. Even though its in the Dutch clip in the picture I just feed it though the loop as often as I use the clip. The loop would rub on the strap in the same relative area.
If this is the way you usually use the clip, you have found the problem.
Rotate the strap so the clip is to the left side of the tree allowing the strap to pass straight through the clip instead of wrapping around it.