I'm assuming you're asking about MileSAAver award availability. Remember, it it is highly unlikely for there to be a flight with zero award availability, period, especially so many months in advance. AA makes every seat on every flight available for award redemptions at the AAnytime level. However, AAnytime awards "cost" many more miles than MileSAAver awards.
That said, AA does not have "blackout dates" in the traditional sense. Every flight is constantly under evaluation by the computers and experts in Revenue Management. Based on historical data as well as actual performance thus far, the staff and computer decide whether to offer MileSAAver inventory.
It is not surprising to me in the least that AA is restricting MileSAAver inventory on JFK-LAX-JFK during the busy, busy travel week between Christmas and New Years. If the OP really wants to use miles to travel during this period on this route, he or she could:
1) spend more miles for AAnytime awards
2) wait to see if MileSAAver inventory becomes available in a couple of months
For what it's worth, I was able to get a Z award on JFK-LAX-JFK during this week in 2010 with only a couple of weeks' notice. But then again, I'm EXP and it was for 3-class F, not Coach.