I have just got myself a NUC also in the past week or so and have been searching for this problem that the original poster and many others have described in this thread.
My NUC specs are:
D34010WYK (Bios 0033)
8GB Corsair Vengeance 1600MHz DDR3L
128GB SanDisk mSATA
And most importantly a Logitech K830 Keyboard
I first thought it was interference from something in my living room where i use the NUC. But i don't have anything in there to really interfere with it. Just a 46" TV that the NUC is connected to via HDMI and a Samsung Soundbar that i haven't actually had on since getting the NUC.
I can bearly get 5' away from my NUC with the K830 before getting intermittent signal. I then tried the K830 on my main PC and it works perfect at any distance within the room i have it in. Whether facing the PC, away from it or even in the next room. So there is no problem as far as I am concerned with the keyboard itself.
I am going to investigate some more tomorrow in regards to disabling the IR sensor and anything else I can think of to (Although I shouldn't really have to do all this considering the price of these NUCS). Don't get me wrong. If it wasn't for this pretty big problem then it would be worth every penny.
I just hope this issue can be recognised and be replicated as a real issue by yourselves at Intel and for there to be a solution soon.
EDIT: Sorry I forgot to add that I am fully up to date with all drivers also.