|Have you dropped the external hard drive since it last worked properly ?|
If you HAVE dropped it, the external enclosure's circuits may be damaged, or the hard drive inside it may be damaged, or both. If the hard drive is okay, it will work fine in a replacement external enclosure.
External hard drives MUST be plugged into a USB port that can actually supply 500ma of current. External hard drives will often NOT work properly when they're plugged into a USB port that's in a USB hub. If the USB cable you're using to connect the external drive did NOT come with the drive, it may NOT be adequate.
Troubleshooting USB device problems including for flash drives, external drives, memory cards.
See Response 1:
Check that out first.
Rarely, not all the ports on the back of a desktop case may be able to supply 500ma each.
If you have a desktop computer, Note that I answered a Topic on this site recently where a guy had an external drive, which does require the full 500ma, connected to a port on the back of a desktop case - it would not work properly when a webcam was in the port next to it, but it worked fine when the webcam was unplugged. Ports on the back of a desktop case often have two ports connected to the same USB controller module that are ports one above the other - you could try connecting the cable to one of those and leaving the other un-used.