Have you tried disabling ultrapeer capabilities (tools > options > speed)? Are you losing internet connection too, or just LW connection? Do you see the firewall icon (brick wall)?

Try file > disconnect, then file > connect. See of a different set of ultrapeers improves things. Do you only lose connection when downloading? Drop back your number of simultaneous downloads.

What type of connection do you have (cable/dsl etc) & what's your speed? You can do a speed test here.
http://www.dslreports.com/speedtest?more=1