... there are a limited number of AAA rates per resort, and some are already gone. I just booked an AAA room only trip for 12/16 - 12/21 and split it between Poly and CR. The AAA rates are gone at CR except for the Garden rooms but Poly still has them. I don't know about other resorts.
On Mousesavers it says that AAA discounts don't usually apply during Holiday season. So I would assume that if you check-in in value season (through 12/19), you would be paying value season rates for your length of stay, and you would be able to apply the AAA discount (if available). But if you check-in 12/20 or after (holiday season), you won't be able to use a AAA discount. This is just my interpretation, so take it with a grain of salt.