Typically AP discounts (actually, all discounts) are blacked out from December 25-31, then resume on Jan. 1st.
Last year there was a free dining offer for Disney Visa cardholders (which also was sent to certain guests in a pin code email) that ended Dec. 20th. If you checked in by that date, you got free dining your whole stay. That was the only time I can think of where a discount was available past Dec. 24th.
I was afraid of that! My oldest DD's bday is on New Years and my husband and I both have a birthday on St Patty's Day...both VERY crowded times of the year to visit!