I'd be happy if the threshhold was 9 rentals in 6 months. Some people have previously mentioned 10 rentals in a rolling 6-month period. A number of times this year, I've hit 9 rentals, only to have one "roll off" just as I was about to rent another car.
If this 9 rentals/3 months, but they only check every 3 months is the case, my next question would be when do they check? At the end of each quarter? I had 9 rentals in the first half of the year, but have not gotten bumped to PS.
Avis would really do themselves a favor if they advertised this program and published explicit criteria. There's a reason air and hotel companies don't say, "Guess how many flights/stays you need to become an elite member!"