iMac unmounts external drives

I have a long-standing problem with my 24" iMac. When running Time Machine backups, the backup would proceed normally until a notice appeared that the backup disk had been ejected improperly last time. At that point, the backup would stop. The drive was definitely not ejected improperly. I erased and reformatted the drive several times, with no results. I have restarted the iMac and tried everything I can think of. At first, I thought this was a TM problem, and then a problem with the external hard drive. However, this behavior now occurs when I use a USB reader to download Canon photos to the internal drive. (The same USB reader works fine on my MacBook Pro.) The problem seems somewhat random; it appears that there is a triggering event by the system, but I can't figure out what it is. I'm running 10.6.7. I spent a huge amount of time on this with Apple while I still had AppleCare, to no avail. Can anyone help?

Apologies if there is a thread for this and the problem has been solved. This is my first post, and I'm just starting to poke around.

Are the drives plugged directly into the iMac and not Via a USB Hub?

They were plugged in via USB hub.

Reason I asked is I have recently had issues like yours and one of my 7 port USB Hubs was causing everything plugged into it to drop. Went to the other hub nothing so far.

I'll keep that in mind as a possible cause. I have other, less-sensitive USB devices (printers, scanner) that I'll plug into the hub instead. The problem was so bad that I gave up on Time Machine and bought a copy of SuperDuper. It's not necessarily the kind of backup I want on a regular basis, but it seems to be capable of stopping the drop out from occurring. Is there a fundamental reason that the hub might cause a problem? If not, I could also buy another hub. (I know the problem was not caused by an accidental disconnect.)