They tend to go pretty quickly, esp. for the deluxes and more "popular" or smaller resorts like POFQ and WL -- just less availability at those to begin with, plus they're very popular. You may have to be flexible with your resort choice or dates. Sometimes it comes down to a choice, you can either have your preferred resort at regular rates, or choose something else at AP rates. Then you have to decide which is more important -- the resort or the rate. So call as soon as you can.
I find it helps the process to have several resort and date combinations that you can be happy with ahead of time, that way when you call you can just run through your options in case your first choice is gone. Then you don't have to make multiple phone calls and sit on hold and lose time by going back and thinking things out. The later you call, I think, the more important this plan can be as things may have already started to fill up and other choices have to be considered.
But even if you can't get what you want, keep calling back. After the first rush of calls when the codes are released people may start cancelling, changing dates, etc. as they work through their plans. So something might open up. Also, if you can't get the AP rate for your first choice, ask the CM if any of your dates are available at that rate for the resort. Sometimes one or two days of your reservation are gone, but you can get the rate for others. You have to split into spearate ressies, but then you can keep calling back to try to get the remaining dates at the Ap rate. Just my shoirt course on AP rates... HTH