Internet problems for Virgin Media customers

For the past few weeks, every night, around 8 or 9 at night my broadband drops down to between 2 and 4 Mbps (from 10). Usually lasts half an hour to an hour and never happens during the day. Also, quite often in the morning I have to reboot in order to connect to the internet.
I have called Virgin three times and feel like I am being fobbed off; could it be my modem is old and not working? But only for short periods at the same time every night? Etc etc. The first couple of times they first said there had been no work being done in the area and then corrected themselves to say there had been work done but everything was back to normal.
I have the feeling they know exactly what is going on and are bullshitting me.

When I was with Virgin ADSL my internet started doing this, and to say it was annoying is an understatement.
Most of my conversations with Virgin were based around them trying to diagnose the fault either when a) it wasn't happening, or b) when it was happening therefore rendering it impossible for them to do any tests. Ultimately they did fuck all about it for about 9 months.

To cut to the chase, Virgin showed themselves to be absolutely non-interested in sorting out anything that couldn't use the old switch on/switch off and phone back later treatment.
So I left them as soon as possible and joined Be Broadband, who were great. But are now owned by Sky so I've got to leave them.

Leave Virgin ASAP is the only advice I can offer, apart from getting matey with a telecoms engineer who could sort it out unofficially for you, if such people exist.