My external hard drive keeps unmounting and remounting itself

Solution 1:

There have been some people using Mac OSX that have had similar problems (see here and here).

The solution that works for many of them (including me) was to just reformat the drive. Since your drive only stays mounted for a short time you will have to do the reformatting quickly.

You can do this with a tool such as gparted, but be careful you can lose data if you don't know what you are doing.

EDIT:
This worked for about a week. I have since taken the bare hard drive out of the case and placed it in this new enclosure. Things seem to be working so hopefully it was just a problem with the case.

Solution 2:

This happened to me when I plugged my external Seagate drive into what appeared to be a USB 3.0 port on the front of my case. Despite having a blue connector, apparently it was not actually a USB 3.0 port. I seem to have fixed the problem by plugging the drive into one of the real USB 3.0 ports on the back of my computer.