I may have found a fix!!!!
I installed the latest graphics drivers released on 3/24/14. I was still continuing to have the same issue, no sound after 15 min or so. Soo, I went to Device Manager and uninstalled only the sound driver (Clicked the check box Delete Driver Software) and restarted the NUC. When I went back to Device Manager it then showed High Definition Audio Device under sound,video and game controllers.
I haven't had an issue since! I can turn off my tv for hours and when I turn it back on I have sound! I was hoping other people could try this out and see if it works for them. Hope this works for everyone! Let me know your results!