You cannot say, "no problems on their end". If Ping Plotter shows no packet loss, when run for an extended period of time (> 2 minutes) and immediately after a disco occurs, your data is not valid.
If your data meets the above requirements, and there is still no packet loss, then it is unlikely an Internet related disco. If you are connecting via wireless, all bets are off due to bit errors occurring, which cannot be stopped. It is the nature of the beast.
If you got here and nothing has clicked, then we need to look at what is running on your computer which could have an impact on the game. Anti-anything can cause problems with game connections. iPod/iTunes also will cause connection problems. Your ISP doing high refresh amounts on your IP address can cause connection issues. That is a few things.
If I still have not hit anything that fits, then we need to get into potential resource issues with the computer itself, possibly driver issues too.
The nature of a disco is the local client (the game on your computer) has lost contact with the server, for whatever reason, so it shuts down. The server never stops talking to your computer. If it did, everyone in the arena would lose connection at the same exact time. Much like it does when we change terrains.