They offer them on a continuous but random basis, and it is constantly changing. It's not like an "AP discount for the month of Aug" or some such - it's individual dates/hotels/rooms based on their current booking level at each hotel and room type. They usually start releasing them about 3 months out (varies), at which point you can check daily or multiple times a day, and you might see different availability at noon and at 4pm, and different availability for a Tues-Fri stay than a Tues-Thurs the same dates.
Best method is to look frequently for any combo of dates that might work for you. You do not need the AP in hand to see or book the rates.
You can also book then change/cancel as availability changes, there's no fee or penalty to do so as long as you're at least 5-6 days out from your stay. You can't make changes between hotels, you have to rebook and cancel in that case, then you get your one night's deposit back within a few weeks.