Time Machine not backing up

I've been using a 2TB Seagate Free Agent drive as my Time Machine drive and it has functioned beautifully for more than a year, but in early November 2010 it stopped backing up and has since done nothing, though it's connected in exactly the same way, is switched on, and tests OK when I verify it with Disk Utility. I've tried "Back Up Now", but though it appears to work for a while nothing is actually backed up. I've reset Time Machine, deleting the plist file, but the drive worked for a little while (I assume it was simply looking to see when the last backup was) without backing up. Until yesterday I hadn't realised this was happening. I'd got so used to it backing up quietly and industriously without my involvement and was surprised to see the last backup listed as 11th November 2010. This is a dangerous situation for me and I would appreciate your advice please.