'kicked off the system', does that mean:

• limewire quits?
• you get disconnected (red dot)?
• ultrapeers drop you?

as far as i know, the latter two don't interrupt your downloads. even if you are disconnected, as long as limewire is open, up- and downloads still continue.

nevertheless, it is peculiar that you should not be able to get a stable connection.

can you be more specific about your system configuration (see other thread in this forum)?