Showing my printout did the trick. When I arrived to pick up the car, the attendant said, "That's strange; I see that you have a reservation, but I can't seem to pull it up." (Same problem I had -- see the original post.) I showed him the printout of my email confirmation, and he re-entered my reservation. He had to do it by manually inputting the rate I had been given, and apparently AVIS really disapproves of that, so he made a copy of my email for his files. He's going to have to do it again when I show up this week.

He confirmed that the start of weekend rates at A4X had recently been changed by AVIS from 9am to noon Thursday. A4X's offering that rate at 9am on Thursdays instead of noon had been an exception to AVIS's usual practice. It's not clear whether it was a computer glitch that AVIS finally caught or some kind of special offer for certain locations (A4X is a non-airport location). Anyway, I had been getting the weekend rate at 9am Thursdays at A4X each month since 2008, but it's over for any new reservations.