I've had this happen with a netgear router. Basically the problem was when using filesharing applications, it used up all of my upload bandwidth, which crashed the computer (and the router as well) everytime I let it run overnight.
The solution was to upgrade the router's firmware and limit the outgoing bandwidth.
You'll probably want to upgrade your router's firmware anyway since it could increase performance and fix bugs. You'll need the model number of your router. (Look on the bottom of the router for it. It will look similar to F5D7230-4).
Then go here: http://www.belkin.co...t/downloads.asp
and type in your model number in the search page. Find the "Firmware Update" link. Download the instructions and the actual firmware file itself. Follow the instructions in the PDF file to upgrade the router.
To limit your outgoing connections settings you'll need to know how fast your outgoing connection is and set that limit to about 85% in the options of Bearshare and Limewire. If you use both Bearshare and Limewire at the same time, the total bandwidth used by them combined should not be more than your total upload bandwidth.
Then again this could be something related to Internet Explorer when you load these programs up...it could be malware or a broken or half-broken internet explorer...