Most likely LimeWire is overloading your modem/Router some how. I am using a linksys wired router which had the same problem when I was running XP Pro until I changed my firmware it took 2 different versions of firmware before I found one that would not drop the connection when running LimeWire. Whenever it drooped the connection I would have to reboot the router in order to make it connect again.
Since I changed the firmware it very rarely happens any more and it has not happened once yet with Vista ultimate. I would suggest looking around for different firmware for your modem/router.
The link below is a good place to start looking for firmware and solutions.
http://www.dslreports.com/forums/all