The last response I received from Apple was several weeks ago. I had sent several sets of logs to them. They appeared to confirm that there was clearly a problem, and seemed to feel it might be a "permissions" issue. Coincidentally, "repair permissions" was completely removed from macOS Sierra. They promised a "hot fix," which I had hoped would be in 10.12.1, but clearly wasn't, though a few have reported resolution with 10.12.1. Since my "Little Snitch" installation resolved the problem for me—it remains resolved even after several weeks and lots of "hard use,"—they have closed my case and I haven't had other communication with anyone from Apple, although I continue to follow this thread.
Recently, some people have reported success using a fix suggested by qkoziol, in this thread: Mac Os Sierra keep logging out !! It is simply deleting com.apple.universalaccess.plist file from ~/Library/Preferences, then rebooting. It has worked for several people and should be completely benign to try. Other fixes have worked for others. None have, unfortunately, worked for others. Apple has endorsed setting up a new account, which seems to work for everyone but, of course, that's no fun! There are other solutions that have worked for yet others, depending upon hardware configuration, that are scattered about the Discussion Groups. Most are referenced in the thread I mentioned above.
If you haven't tried it, I would suggest trying qkoziol's solution. If that doesn't work, and you use Razer Synapse, DuetDisplay, or your problem occurs exclusively with Chrome full-screen video, there are other solutions out there. You can always try my "Little Snitch" installation, which worked for at least a couple of people, including me, but not for lots of others. I don't believe it's the program, itself, that did anything, but something that it "fixed" during installation. I've posted the "Little Snitch" installation log elsewhere, and sent it to Apple. Clearly, this is a problem different groups of people are all getting to via different mechanisms. I'm sad to say that Apple Support, while very well-meaning, courteous, and helpful (at least wanting to be), has not been more forthcoming with a root cause and universal solution.
Worst case scenario: Migration to a new user account; that seems to universally work. I'm sorry I don't have anything else to offer.