Earlier this year, while camping some 600 miles from home, one of my handles did the same thing. It pulled right off the threaded shaft. I was able to find an RV parts store and purchased a new Valterra handle. However, there was a problem.
The cable end had that metal pin you are talking about. I thought, "no problem" just pull it out. WRONG! That pin is welded in place. It cannot be removed. And with that pin in the metal shaft, the new one would not simply screw on.
My solution? I had a metal grinder wheel for my electric drill and I was able to grind that pin down to the threaded shaft. The only problem now was, I could not get it down far enough for the threaded new handle to screw on enough to actually be secure. I did not dare grind any more, for fear of actually grinding the shaft-rod.
However, it was down far enough I was able to force the handle on and then give it a quarter turn. This worked OK for a short while.
Fast forward a few months and that handle came off also. A simple push and a twist and it would catch on that ground down pin again. But eventually, the new plastic handle wore also. Now, it would not catch any more.
Desperate times call for desperate measures, and the Good Lord gave me the right kind of wisdom to use at just the right moment. ... never do I get the "Ah-Ha!" moment early and usually, that inspiration leaves when its done. Thank goodness for photos!
So, here was my solution.
Behind the ground down pin was a nut. The nut could not be removed because that ground down pin would not let it pass. That nut actually became very useful.
I then has a small piece of 1/4 inch plywood (I was using for something else), and I was able to cut it into a circle, about 3 inches in diameter and drilled a hole in the middle to slide over the cable shaft. But! I needed the plywood behind the nut. So, I cut a split in the plywood and was able to wedge it so it would slip over the shaft and slide into the drill hole.
I then drilled a couple holes in the original handle. I tightened that back nut up as far as I could, pushed the pull handle on and ran wire behind the plywood and through the drilled holes and tied it down tight.
When pulling the valve, I pull behind the plywood now ... NOT the handle. When shutting, I push on the handle .... NOT the plywood.
It worked so well, I have no intension of replacing the cable now. No need to! I also painted that plywood black to help protect it better. In the photos below (which I just took a few minutes ago), I need to spray paint it again.
The description may sound difficult, so photos may help more: