In my experience, 30 minutes for a domestic connection in Miami is pushing it. For international connections, 30 minutes is WAYYY too short. Immigration always seems to be very busy in Miami, though having an INS PortPass enables you to cut a lot of time off the process.
Note that AA will *not* put you up for the night if you miss a connection due to an illegal connection. And as others have stated, AA.com doesn't always consider minimum connection times, etc.