'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)?