Could an old worn out clutch be causing the cable to snap?
The wear on the clutch has nothing to do with this problem. What is causing the cable to snap is the way the cable is routed in the engine bay. Your cable has been moved from its Original position and now has a bend or a sharper turn in it. Check the cable is free to take a unrestricted path and make sure that it is not kinked it attaches to the gear box housing.