Bad wire tripping GFCI

I've had one GFCI circuit that tripped intermittently for years. It might run for months, then trip. It would always reset, and then may not trip again for days, weeks, or months. It tended to trip when there was an electrical or rain storm, but that was not an absolute thing. So, it was a pain. Didn't matter what, if anything was plugged into any of the daisy-chained outlets. Well, it finally recently got to the point where it would not reset. Just to double-check, I tried a new one, same thing. SO, I started to take receptacles out, disconnecting wires and isolated it to a problem between the second to last and last box. Right now, I disconnected those leads and capped them isolating that last outlet. I can live without it in the interim. My guess is that there must be a pinch or nail or something impacting the wiring to that last one.

What would the normal practice on this be? I'm guessing, just run a new cable and not worry about it. I'd rather not tear the walls all up, and there's no way to tell how the silly thing is run as the ceiling in the basement is finished.

If I read your post correctly you want to run a new romex and abandon the old one. No problem with doing that. I usually tape up the ends of the old wires and tuck them to the back of the box.