Might be that the HDD inside it is dying. If you aren't concerned with warranties, you might try opening up the external's housing to pull out the drive. Then, you can try hooking it up to your computer directly (provided you have a spare IDE or SATA cable and a spare plug from your PSU to power the drive).
If that doesn't work, you can try sticking the drive in the freezer overnight (longer is better) and then try hooking it up inside your computer again. Probably a good idea to stick it in a ziplock bag with a few sheets of paper towel (to try to fight the condensation that will occur) both when it goes into the freezer and when you hook it up again.
The freezer trick usually gives you about an hour at most, so if it comes to that...work fast. You might be able to do the freezer trick a few times (maybe).