Common causes of Broadband disconnections:
USB modem not getting sufficient power. The modem requires 500mA to function correctly. That is the maximum available on a USB hub. As a hub normally has two ports, the second port must not be used. The modem must be connected directly to the computer, not via an external hub.
The computer may be configured to turn off the modem to save power. In Device Manager, find the modem. It may be under Network adapters. Select Action, Properties, Power Management. Do a similar check on any Routers you are using.
Phone extension cabling may be prone to induced interference from mains wiring. If necessary, run a temporary extension lead to rule this out.
Radio interference from cordless, including DECT, telephones. Turn them off to prove.
Radio interference from taxis, CBs, neon lights, streetlights, etc. If this is suspected, BT can fit a suppressor to the incoming line.
There may be a clue in Event Viewer. Start, right click My Computer, Manage, Event Viewer, System. Select an Event, Action, Properties. You can send the data to Microsoft for more detailed information.