Do you use a USB modem? If yes then it's very easy for your modem to have issues when heavy traffic is put thru it. See 3.4 USB-based modems/routers Scroll down to 3.4
Other than that ... as BP said. Also modems can lose communication with the computer if it is overstressed. By the way 32 MB ram is not sufficient for both your system & LW. See bottom of http://www.limewire.com/english/cont...loadfree.shtml 64 MB is recommended bare minimum ram.