Folks with the unresponsive iPad Pro touch screen issue…
When it starts misbehaving, take any cases/pencils off your iPad. Set it down on something like a wooden table or something non-conductive. Don’t hold it, just use some gestures on the screen.
How does the touch-screen perform?
After some testing I’m fairly confident it’s an electrical issue. I can get the problem to appear and go away at will, but some additional data points would help.