The class has to be available, not "any seat". I recently wanted to change a early Monday 1am LAS to IAH flight to later in the morning (by phone, by the way). The agent said there were seats available on ALL flights later that morning, but the 9:30 flight had no seats in my original fare class. I did have my choice of 4 other flights, though.

I have resolved, however, to stick to the 1 am departure from now on. I could not believe the security line in LAS on Monday morning.