However when I play content 4K 60hz it sometimes drops out, for half a second the image gets black an reappears. Even in the GUI it shows this behavior. With the 30hz settings it behaves normally as intended. So is my NUC too slow to display 4k at 60hz?
Unless there's some driver issue (that we won't know about) the GPU and DRM drivers should handle 4K@60 fine. However 4K@60 requires considerably more bandwidth on the HDMI connection so the common weak-link is the HDMI cable. Pretty much any old crap HDMI cable will handle 4K@30 but "certified" cables and sometimes specific HDMI ports on the TV are required for 4K@60.