VM running Sierra 10.12.3 in Parallels 12 stops responding to the mouse
A workaround with this is to open Apple Remote Desktop, and screen share the Mac VM. At least doing that will keep me from losing work that I have started in the VM.

I have contacted Parallels support about this many times. It happens on both of my Macs, and it has been going on since I upgraded to Parallels 12 last year. It's still happening with Parallels 13. Several people at Parallels claim that this is something that the engineering team is looking at, but if they are, it's low priority to them.