Decades ago, a plumber used what looks like a self tapping saddle valve to connect my refrigerator's ice-maker's water supply pipe to the main cold water pipe under the sink. Now the saddle valve is leaking from the self-taping screw. If I turn this screw just right, I seem to be able to stop the leak though I do not know how long this will last. Any little twist of the screw and the saddle valve leaks again.
How do I repair this leaking saddle valve?