I have been having trouble with a 500gb Seagate external hard drive ejecting itself during Time Machine backups and when drive is connected but not being used. This is a drive I have been using for a couple years at least, and with no problems.
This problem started today when I was backing up my "non-media" files(everything but photos and videos) and only got through 75 of 175 gb when the drive ejected itself.
This problem got progressively worse until it was ejecting itself in as little as 30 seconds after hooking it up through the USB port.
I called Apple Care and they seemed to have fixed, I've completed the Time Machine backup. The fIx, do a "NV Ram" or NVRM Reset:
1) Shut down everything, close all windows, do a "Shut Down", but when the Shut Down window pops up, uncheck the selection "Reopen Windows When Logging Back in". Then click Shut Down.
2) You'll need two people to complete the next step.
While one person is holding down the Option, Command, R, and P keys the other person pushes the start button on the computer(iMac 20" mid-2007 unit in my case), and then continue to hold the 4 keys down until one low volume chime, 2 loud chimes occur, and then let go of the keys.
After this my Seagate has remained connected even after a 30 minute Time Machine backup operation was completed to it.
Thankfully! Hope this helps others, and don't know if this was already covered earlier.