I had a similar problem with my NC23 in that it kept cutting out for no apparent reason and then would refuse to restart but I could bump-start it. I tried a whole host of things including replacing the reg/rec, new carbs, cleaning all the electrical connections. In the end, it was a defective pick-up. I haven't had a problem with it since and it starts first time, every time on the button.

I had a problem like this with my nc29, i had new battery new reg rect and allt eh connections were sound. In the end it was the generator that had gone as the bike was purely running on the battery once it got back to idle the it couldnt sustain itself so it cut out. Do a charging test on the bike to see if you generators nakered if so will cost bout £150-£180 to do it all at a garage. My bike is now runnin sound as a daisy

Hope this helps