I've had this problem a couple times on different Sculpt keyboards (one I use at work and one I use at home). Both times I ultimately discovered that the problem was caused by a key getting stuck (most recently it was the F8 key). Presumably when the key is pressed repeatedly and no other keys are being pressed to interrupt it, the keyboard decides to disconnect.
Both times when I fiddled with the sticking key a bit and to get it unstuck, the problem of the keyboard disconnecting (despite the number pad working) went away - no more taking the batteries out and putting them back in every time I stopped using the keyboard for a few minutes.
The design of this keyboard seems to have an issue with keys somehow getting caught in the pressed position, but fixing that when it happens generally solves the problem of disconnecting.
IF AT FIRST YOU DON'T SUCCEED, TRY TO UNSTICK THE KEYS!
I was having the same issue with the keyboard not responding to any keystrokes, but the separate numeric keypad worked fine.
After deleting and reinstalling the drivers, I followed the advice to 'unstick' the function keys. I went across the top line of function keys rapidly tapping each key with some sideways and up and down force, until suddenly the keyboard responded.
In support of the stuck key syndrome diagnosis, I noticed that this occurred after the previous night's visit from the office cleaning staff. I left the keyboard out overnight, and the cleaners wiped and/or vacuumed the keyboard. I believe their action caused a stuck key.
So, I happily retrieved the batteries from my trash can, since they were not the problem, set aside the clunky temporary Dell wired keyboard for future emergency, and resumed typing.