Please take each of the following steps that you haven't already tried until the problem is resolved.
1. From the menu bar, select
▹ System Preferences ▹ Energy Saver ▹ Power Adapter
and uncheck the box marked
Put the hard disk(s) to sleep when possible
if it's checked.
2. Some external drives ignore the Energy Saver setting and spin down anyway. The application "KeepDriveSpinning" from developer Jon Stovell may help in that case. (Credit to ASC member dsrtmacusr for this solution.)
3. If the drive is connected to a hub, connect it to a built-in port on the computer.
4. If the drive has more than one bridge (e.g., FireWire and USB), try another one.
5. If a firmware update is available for the drive, apply it.
6. Contact the drive manufacturer to see whether there's a firmware setting you can change.
7. If you installed vendor software for the drive, uninstall it.
8. Triple-click anywhere in the line below on this page to select it:
/Library/Preferences/com.apple.TimeMachine.plist
Right-click or control-click the highlighted line and select
Services ▹ Reveal in Finder (or just Reveal)
from the contextual menu. A Finder window should open with a file selected. Copy the file to the Desktop. Then move it (the original, not the copy) to the Trash. You'll be prompted for your administrator password. Restart the computer and recreate your settings in the Time Machine preference pane. It will show that you have no backups. Don't worry; that's expected. Run a backup to test. The backup may take much longer than usual. If TM now performs as expected, delete the file you copied to the Desktop.
9. If none of the above steps resolves the issue, the drive is faulty. Use another one. You may be able to salvage the mechanism of an external drive by installing it in another enclosure.
