Ubuntu 16.04.2 and 16.10 screen goes black randomly for a second

The X server in 16.04.2 point release has been back-ported from 16.10. That must be why you're facing the same issue on both of them.

I had been experiencing a lot of random flickering as well, after the upgrade.

Removing the new X stack seems to have fixed it:

sudo apt remove xserver-xorg-core-hwe-16.04 xserver-xorg-input-all-hwe-16.04 linux-generic-hwe-16.04 xserver-xorg-video-all-hwe-16.04

However, ubuntu-desktop will also be removed!

So, you need to do the following straight away:

sudo apt install xserver-xorg-core

sudo apt install ubuntu-desktop xserver-xorg xserver-xorg-video-all xserver-xorg-input-all libgl1-mesa-dri libgl1-mesa-glx

Source

I had a similar problem running Ubuntu 16.04 with Intel Xeon E3-1200 v2/3rd Gen Core processor Graphics Controller (rev 09)

My monitor was blanking randomly and unpredictably for a few seconds, mainly after coming back from the suspend state.

My solution was to make changes in the system settings. Open the settings program and click on Devices, then select Displays. I lowered the refresh rate from 60 to 50Hz and the problem has disappeared.