I wouldn't bother wrapping tape on stuff like this, it might actually make it worse.
That connection doesn't need any weather protection. The machine screw can loosen up because it's biting into what is essentially a thick aluminum wire, and over time and thermal cycling, the stainless steel bolt will lose solid contact with the aluminum.
It's not the clamp that's at fault, it's the material of the ring. Tape won't help.
I've used Ringo antenna since they were first introduced to the market about 42 years ago, and discussed the design a lot with the inventor, Les Cushman W1BX (who ran Cushcraft). He recommended that if anyone wanted to make this a more "permanent" antenna, replace the aluminum ring with solid hardened copper.
My take is, for a "very permanent" installation I expect to last many years in the weather (through thousands of thermal cycles and such), use better antennas that were really designed for it. If I install a Ringo in a place where it's serviceable, I just do annual maintenance on it, including tightening stuff that comes loose.