I found it interesting--I was looking for 12/6-12/17 at the Pop. Initially I called and they said it was available, but that there was some technical difficulty that prevented them from finalizing the reservation. They told me to call back later that day.
I called back later that day, and now they said that there was nothing for the Pop for those dates at the AP code, and that there was only ASMu and ASp. Frustrated, I put a courtesy hold on those dates at ASMu.
I called back again, right after, and this time was told that there was nothing for anything but ASp. This time they said that there probably had been no availability for Pop earlier either, but that it was the technical error that made it look like it was available.
After doing some fuming, I checked online. After playing a little with the dates, I found that I could get the AP discount on 12/7-12/17, so I booked that, with the expectation that I'll either pay rack for 12/6, or stay a day over at ASMu before moving to the Pop.
So what I take from this is that, apparently, if a hotel's not available for all of the dates you ask, the computer doesn't display to the CM which specific days are available--otherwise I assume someone would have said "hey, it's available for all but one of your days." Of course I also found that the first CM was very nice and helpful, but the two I got later in the day were very abrupt and would only answer direct questions, volunteering no additional information or pleasantries. I was holding on the line for the survey at the end of one of the calls, when the CM came back on line and asked what I wanted. When I said I was waiting for the survey, she just said "oh" and clicked off.
For the best chance, I would advise checking all permutations of what you would accept online right before or even during your call, because the CMs don't seem like they can/will do it for you, and that way you can just ask them for what you think is available. The CMs in the AM also seem to be better disposed than the ones in the PM, from my sample size of 3.