Symptom: Mouse dies intermittently, Windows makes the "USB device disconnected" sound, and the lights on the mouse go out.
Problem: Probably a broken wire in the cord.
Try it on another PC to make sure it is the mouse that is the problem (not your PC). If the problem is the same on the other PC, get the mouse replaced or fixed.
Less than 30 days since purchase, you need to exchange it where you got it.
After 30 days, you would be covered under the 1, 3, or 5 year warranty from Logitech. RMA info.
If you are out-of-warranty (or don't mind voiding any remaining warranty), you can probably do some soldering and shorten the cord to remove the break (probably near the mouse), or replace the whole cord with another USB cable (salvaged from another device or buy a USB extension cable to splice in).