Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
You'll never find CX award availability on aa.com, because aa.com does not support award redemptions on CX (or a dozen or so other AA partners). You must call AA -- and pay the telephone-ticketing fee -- to book award travel on CX with AA miles.
The CX award-seat availability you see on ba.com should match the availability that an AA agent can see.