Sylvia,
it looks like the Intel video driver is the problem.
I now have the Logitech keyboard and mouse connected over the unifying receiver for some time (receiver connected over USB extender cable to the NUC), and it has been running for at least 8 hours without any issues. I am using the Microsoft's "standard VGA graphics adapter" driver. The 7260 WiFi/BT card is disabled in device manager (both WiFi and Bluetooth).
As soon as the Intel video driver release 3496 (or 3412) is installed, the NUC becomes unstable (freezes and corrupts the screen). I have noticed though that there are no more "poweroffs" and automatic restarts - now, when the Intel graphics driver is installed, the NUC just freezes and corrupts the screen. Then I need to force power off manually.
I have re-enabled WiFi and BT and so far have the NUC running normally for more than a few hours. I will continue testing (takes time as the freezes are/were not dependent on any particular action) and report back. But so far, I would say that the video driver seems to cause problems.