As others have said just keep calling and checking availability. We just had to cancel our reservation for the week of ThankGiving 2013.
We booked it last year while at the Fort for Thanksgiving, then my work schedule changed and we had to cancel. This happens all the time.
They also have last minute cancellations. We met a couple last year who had never been. Decided the day before, they wanted to spend the week at The Fort. They called on Friday, and were in their site on Saturday for the whole week... And that was the week of TG. One of the busiest weeks of the year.
Bottom line... Persistence can pay off!
As for discounts... It has been said that "Disney" and "Discounts" cannot be said in the same breath. As others have indicated their is the AAA discount, but not sure it gets you much. I have heard the military discounts are significant.
Disney's just not one of those places I associate with discounts. As a co-worker once told me...
"When you walk thru the gate, Mickey Mouse is going to grab you by the ankles, turn you upside down, and shake all the money out of you pockets! ... And if you're OK with that, you're gonna have a wonderful time!
No saying was ever more accurate!