There seems to be a glitch at the moment, we've had a number of threads on this recently, here is the one with the most detail (see end of thread):
AA [award] space on BA website
What you should do is check on AA that Milesaaver is available on a particular direct flight (not connection), check BA.com, if it doesn't show either refresh or go forward a week and then back again. Or just ring up, the agents are hopefully aware of the website's glitch in this area and can waive the fee.