Hi Mattias, I believe more troubleshooting is needed in order get a chance to answer such question.
Perhaps you may want to try with a different Intel® HD Graphics driver: https://downloadcenter.intel.com/Detail_Desc.aspx?agr=Y&DwnldID=23886
Or updating BIOS (incrementally): Intel® NUC Boards and Kits — BIOS update instructions
Does the issue happen with different video formats (mkv, avi, mpeg)?
Are you connecting the display with any type of adapter/converter or a straight cable?
I connected a HDMI switch between the NUC and TV.
When the screen turns black, I can see at the HDMI switch that “connection led” blinks.
It’s as it lost it HDMI connection for a second.
When the screen was black, I started a remote desktop towards the NUC.
When I do that, the picture went back on the TV.
It seems that it has something to do with lost HDMI signal?