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By removing the USB 3.0 drivers you will have the USB 3.0 ports working as 2.0 version.
Does this problem occur with earlier BIOS version?
You could downgrade BIOS version if you run BIOS recovery, see here for instructions: Intel® NUC Boards and Kits — BIOS Recovery Update Instructions
File name: WY0028.BIO
After reading a bit more other posts it seems to be caused by interference :
I'll try to find a usb extension cable and check if it solve the issue.
I am also having this exact issue. I'm running all the latest drivers and the latest BIOS (033). It's definitely not interference since I have two computers on two shelves and the USB ports where the Logitech receiver gets plugged into each computer are just 7 inches apart. I've tried every USB port on the NUC with no change in performance. When attached to the NUC, the keyboard works up to about 6 feet away from the receiver and then begins stuttering and missing key presses; at 8 feet, it doesn't work at all. When attached to the other computer (a USB 2.0 port with a 6 inch USB extender cable, I might add), I can walk into another room and the keyboard works flawlessly.
UPDATE: Some further searching led me to this thread: Logitech K400 keyboard laggy and jumpy on my i3 NUC
I moved the extender cable to the NUC and the keyboard works fine. To see if it was positioning, I tucked the extender in as many positions as possible, including directly in front of the IR window, literally tucked completely underneath the NUC itself, around the side, etc. Absolutely no orientation causes the issue EXCEPT when the Unifying receiver is plugged directly into any of the NUC's USB ports. To cover all my bases, I removed the USB extender cable from the other computer and plugged the receiver directly into the USB port and everything still worked fine. This would seem to indicate the issue is with the NUC design (case or hardware layout, perhaps).
UPDATE #2: I noticed that my non-NUC computer allows some space between the edge of the computer case and the receiver cover, leaving about 1/4" of the USB plug itself exposed to the air. The same is true of the USB extender cable I'm using. However, on the NUC, the receiver is flush against the case, leaving no gap at all. I attempted to leave a bit of a gap, but I couldn't get anywhere near 1/4" before it was considered unplugged. Looking at the NUC case, I see that there's about a 1/8" gap between the case and the end of the USB port of the NUC. I would guess that between the thickness of the NUC case and this 1/8", there probably is 1/4" of space to be had. The rear USB ports on the NUC do not have any space between them and the NUC case, but there is still probably about 1/8" between the USB edge and the outside of the case. Cutting the NUC's case to enlarge the hole around the USB port by ~1/8" on all sides might resolve the issue, but I'd hate to ruin the case for nothing.
Until the case is redesigned, the solution is quite simple (thought a bit ugly): Get a short USB extender cable. The USB cable I'm using is 6 inches.