I had that issue. When I installed the firmware update the first time, I got a sleep of death but it didn't show up in Windows update anymore.
Then I kept getting SODs regularly, ie it'd die as soon as I closed the keyboard.
Did a quick refresh while keeping all data intact. Ran Windows Update and the firmware update still showed as not being installed so I installed that by itself first before everything else. Got all the other updates, it seemed fine for a bit but would SoD over night. Then there was a Skype update released the other day on Windows Update that seems to have fixed my SoD issue completely.