Here's what happened to me trying for AP discount this a.m.
I finally got through, and was told the system was down. Eventually got called back after they were open for 1 hour. They had no preferred rooms for AllStarMovies during our stay. Had to call the wife to see if she wouldn't mind switching to standard room at Movies. After talking about it called back. It was approximatley 25 minutes after my previous talk with disney ( 1 hour and 25 minutes after they were open ) and they now had no AP discounted rooms available at All Star Movies for our stay.
As WDWHound said and the CM explained to me on the phone, they only set aside so many rooms for each discount, when they are gone, they're gone. I mentioned the BAT code. She said it was in the system but able to book until tomorrow. She said I should start calling as soon as they open tomorrow as they were so busy today.
Also, some have mentioned how as people change their reservations, rooms may become available. So if tomorrow you can't get room only, try asking for the AP discount. Someone who booked AP rate today but doesn't have an AP yet, might get a room only discount tomorrow and cancel their AP reservation, freeing up a room for you.
Good luck.