Do you have any anti-virus or anti-spyware utilities running in the background?
I use Virgin broadband as well, (I'm in the UK), and have no connection cut-offs like you, except once a day when I leave my computer unattended and my AVG anti-virus runs a scheduled scan. After that I sometimes have to right click the broadband network icon in the System Tray and select Repair. it is as if the virus scan disables the connection.
Is your AV, (or even anti-spyware), carrying out regular scans more than once a day? It wouldn't be normal for a scan to be done every few minutes, but there seems to be something cutting in every few minutes or so.
In any case, check for viruses and spyware.
If you have a firewall I would not expect that to cut you off at regular periods. The firewall either lets the internet through or it doesn't, period.
If you can get a time of a cut-off, look at your Event Viewer for that time and see if there is anything relevant listed. Event Viewer can be accessed through Start > Run, type in eventvwr.msc and click OK. In the Event Viewer console look for any warnings or exclamation marks, highlight, and double click for more information.
Mark