I would suggest that you test the NUC directly to the monitor to see if it behaves the same, also, let me know what graphics driver version you have installed as well as the BIOS version.
Behavior is the same graphics driver is 4251. Is there a way to find BIOS version in windows?
I've had similar issues but it's not consistent as your seems. These devices seem to have a lot of sleep/wake up bugs. I have have a 5i5RYK and the sound gets muted once in a while when waking from sleep and won't "unmute" until a reboot. I'm running Windows 10 64bit. I'm passing audio through the mini DP to the monitor which has an 3.5 mm jack.
Intel is aware of the issue related with Windows 10 and the Intel® graphics, our engineering department is working on a new graphics driver. You can post your issue and see more information here: