I had the same problem myself. The fix was to replace the battery in the phone. I ordered a replacement from Amazon.com. As I also had had to replace the screen just before that (my wife face planted the phone on a rock), I already possessed the required tools to take it apart - they came with the replacement screen. It needs a very small hex driver, a very small philips driver, a spudger and the SIM pin (or something similarly pointy, such as a needle, to remove the really long locking ping that runs the length of one side of the phone)
My wife's Surface Pro 4 Core i7 model had the battery bulge, and after an hour or so of use, it would cause the touch screen to malfunction (presumably from the pressure on the glass). We replaced it with a just-discontinued Surface Pro 7 from Best Buy at the time (we got the display model) and she's had that ever since. I set the Pro 4 aside with a plan to try and replace the battery at some future point. That point was this week!
I verified the battery was completely dead and then I threw the whole thing in my oven at 175 deg F. The pressure from the battery did most of the work freeing the glass from the adhesive, making it MUCH easier to remove the glass without breaking it. I DID damage one of the antennas removing it, but the replacement antenna bar on eBay was only $10. One of these and the iFixIt battery kit (with tools) allowed me to complete the repair and it is now working beautifully.
