I just updated to the latest version of Nicehash, and the latest version of NBminer, and the behaviour remains.
Of note: I manually update the Avast program (virus updates are on auto). Hadn't done it in a couple of months (I know, I have reasons). Just did an update, and after that this problem started. So it is some change in the way Avast handles these files in the last several months that seems to be the cause.
I've sent both the old and the new version of NBminer for analysis. But the fact remains that even with explicit exceptions set to leave it be, Avast keeps quarantining the executable.