What I have found is that the 'basic brawl' on the 'brawl with anyone' function isnt necessarily broken but it just takes a long time to find a person to play because most are just playing with friends(people they have traded friend codes with and set up organized games with said people). The disconnects and error codes that knock you off after a couple minutes I have also experienced but only when trying to find a random game with 'brawl with anyone' just because the connection times out trying to find someone. This happens extremely less frequently when playing with friends because you can coordinate the game to happen, i.e. talking on AIM and saying you are going to make the room then your friend joins right after you make it. I have found doing friend brawls take less time to set up and doesn't give the connection as much time to time out or give you those error codes that knock you off.
Lots of people have cought on to this and just play the friend battles just by posting here and having people respond to them on AIM with their FC's so that they can communicate before, during, and at a later time for more brawls. I reccomend you just try and do that. Make a thread saying what you want, a screenname to a messenger program like AIM or MSN so you can keep in contact with your buddy and also so you can coordinate games with them, and to exchange FCs.
I hope this helps! Happy smashing!