I manage the Spaceduck servers (Europe) for the PS2 for fun (SWBF 1 and 2).
Players get booted automatically from my servers if their ping is over 300; besides, any ping over 250 makes the game not worth playing for that player. A high ping is usually the reason for being booted immediately from any PC-dedicated server.
You can find out your own ping by pausing the game ("start" button) then choosing "player list". The ping is related to the time in milliseconds your PS2 takes to respond to the server. So if the ping is 500, that is half a second and your game will be very jerky and slow to respond.
So far, sessions have only ended prematurely when the SWBF software has problems with auto-turrets; I have been told that this also occurs in single-player mode (offline) games.
May the force be with you! (Especially if you just sat down and your TV remote control is on the other side of the room).