Media Server :: Stream Works Outside Firewall But Not Inside Firewall?

I have my stuff set up and everything works fine except for a very strange glitch.When I use the internal IP address (192.168.###.###) from a machine on the internal network, it works fine.When I use the external IP address (209.###.###.### which eventually maps to that internal IP address) from a machine out in the world, like at home or a hotel or a clients site, it works fine.But, when I use the external IP address from a machine on the internal network, everything works except the flv file doesn't stream. The HTML page displays, the swf player displays, but the flv file doesn't stream; the swf player displays the message "Connection Error. Please press Play to try again."
 
What could possibly make this happen? To me, it seems impossible. Could there be a setting in FMS that would cause this sort of thing? I very much doubt it is a firewall issue, because if it were, then the file wouldn't stream from outside the firewall.