Not sure whether this is the primary cause or a potential solution to this "unresponsive screen" issue.
After applying various screen protectors, there are times that the screen starts becoming "unresponsive".
I think there are some things in common as the issue occurs:
1. The iPad Pro is in a Folio
2. The iPad Pro is placed on a plastic surface or cotton material
3. The user only use one hand to touch the screen
I propose that when your screen becomes unresponsive with a protector on it, you simply need to use your other hand to touch any part of the bezel and maintain your original touch operations with your right hand.
i.e. use one of your left-hand fingers to touch any part of the black bezel and the screen responsiveness will be back to normal as you touch with your right-hand fingers.
My conjecture is that when the iPad Pro has a folio on it, the electron accumulates to the top of the surface which causes the unresponsive issue.