hard drives improperly ejected

I have an iMac (early 2009). It recently started to eject external drives attached. I have replaced my hum without help. I have plugged directly into the USB2 ports, but it still ejects. Ir I unplug the drives and replug, it starts again.
I have both Seagate and Western Digital
Any ideas?
mjshack

Note 2 of the drives are externally powered
mjshack

Do you know how to properly eject mounted drives before powering down/sleeping? If not, you are destroying your drives' directories and they will eventually lose all the data on them.

Chas, read his OP more carefully. The drives are ejecting by themselves. He is doing nothing to eject them! He even directly connected them to the USB ports on iMac and they still eject by themselves.

dtravis7 - you are correct. My only solution is to eject the drives whenever i don't need them One is Super Duper backup that I schedule manually and the other is a manual backup that I do of important data and photos (I am an amateur photographer and do a lot of photo corrections). The 3rd drive is Time Machine which I would like to leave on.
mjshack

Do you get any dialog message saying they were ejected incorrectly?

Regardless, I'd suspect a bad cable or connection of a goofy power adapter if they are externally powered. Or maybe an SMC reset would help???

Sure lot's of discussions on the problem, including a 63 page one that seems to be for 10.6.8 users that finally ends at:
https://discussions.apple.com/message/27091624?tstart=0#27091624

I didn't notice what OS X version is being used, but lots of hits with a search:
https://www.google.ca/search?client...&oe=UTF-8&gfe_rd=cr&ei=NT-CVJPmN-js8we9zIK4Bw

Personally when I am finished backing up with SuperDuper, always eject and pack away.