For what it's worth, I managed to get hold of Avis customer service, since I've had my share of problems getting miles to post for my rentals, and I was told that they're having a technical problem that wipes away the FB number during their database updates. Apparently, these updates are scheduled every three weeks. To bypass this problem, I was told to be sure to enter my FF number for every reservation.

Not quite sure how this explains miles being only partially credited (ie. base miles, but no online bonus, for instance).