Need more info...
How are you connecting to the Internet? USB modem, router, 56K dialup, etc?
Wired or wireless?
What exactly "goes down"? Your LAN, router, DSL line, telephone line, or what?
What sort of storage device are you using? Does it have its own mains PSU, or is it drawing power through the USB port? Maybe via a USB hub?
To hazard a complete guess, I'd say it might be you're using a USB powered device through a hub and it's pulling the power down to your USB modem...
ROGER - G0AOZ.