This is an AA reward question that is best dealt with on the AA forum. I see you started a similar thread there:
http://www.flyertalk.com/forum/ameri...im-direct.html
Also see this thread on the AA forum:
http://www.flyertalk.com/forum/ameri...-miles-12.html
There you will see that phantom availability on ba.com is very common.
You will also find numerous threads on the BA forum discussing problems with finding and booking LAN reward flights.