How do I repair the touch sensor ground fault?

Replace affected door handle. They fail, apparently they weren’t properly water sealed and the elements then kill’em after a few years.

I’ll second that. I’ve had 4 fail in the past 7 years on 2 Q7s. Newer Audis even my 2015 S5 have a different sensor that works on proximity rather than a push button. Apparently they are much more reliable.
Be aware that the ones on our Q7s can drain the battery when they fail. Doesn’t always happen though. Mine never did.