Most likely its cause Sony has not made anything worth a damn in 20 years. Seriously just about everything they make anymore is trash.
Did you call Sony Tech to see what they say?
Did you try to download latest Ubuntu (currently 15.10) and burn on a DVDR/DVD-RW and boot from that and see if you still get the same problem?
My experience with linuxsupport, well ubuntusupport, and NUC is that its the Ubuntu version released after the NUC was released that fully works with all the internal devices of the NUC.
Like the D54250WYK didnt fully work (that is without issues) until Ubuntu 15.04 was released (D54250WYK was in stores spring 2014).
Other than that does your TV have the latest firmware installed and what is its settings regarding HDMI and such (dunno about your specific models but some TV's have various "linksync" (various propertiary stuff to use a single remote for all lets say sony devices) which you can disable to see if it works better and such)?
I was checking the manual of your TV, and a possible troubleshooting would be to check if you are using a cable with the specs they request.
Cable recommended by Sony: use a HIGH SPEED HDMI cable that supports speeds of 18 Gbps.
Also, the firmware update could help with this situation.
I would like you to verify if the HDMI output from the NUC works with a different TV still, also if the HDMI cable used can be used with other devices in your TV.
Related information found here: Help Guide
I look forward to your outcome on this.