|This is a long shot - pending input fro others...|
It "may" be the onboard controller for the external drive case is acting up...
Not unknown for the usb port to act up; often becomes disconnected from the motherboard; and on occasion that actual on-board electronics fail.
You might get hold of (as in buy) a sata-usb adapter cable set. remove the drive from its current housing; connect to your computer using the adapter cable.
It "may" work; and if it does... I'd instantly duplicate anything on the drive to that's important (usually photos etc. at least) to DVD - just in-case there is a problem with the drive at some future time (even now).
I have one by this company/vendor; it works a treat; and isn't expensive. A useful time to have at any time in one's tool box...
Meanwhile - don't write or do anything to the drive as is; certainly do NOT initialise it... - as you "will" lose all data in the process.
Have a read of this article - carefully note the first option - which they advise NOT to pursue if the drive has content you wish to preserve/recover etc...
There are others likely much more "up" on this issue than am I so hang about a wee bit too for their input. And maybe get the sata-usb cable as well and see if it helps as above?