I'm assuming that at the very least you would have made mention of the fact that the USB Lead is less than perfect.
Now depending on just how much importance you place on the [b]Priceless Data[/b] it is possible to recover it but it's not cheap.
So start with the obvious and change the USB Lead and the Enclosure It just may cure the problem.
But if it doesn't you will need to take the Drive to a Data Recovery House that is capable of reading the [b]Actual Platters.[/b]
This means that the drive has to be dismantled and the Platters Removed so you need a Data Recovery House that can do this and not just one that works with Iffy Drives. On Track can do this and as they are the only ones that I have had first Hand experience with they are the only ones that I can recommend. The last time I had to do this with a Dead Drive it cost 46K AU but that was a Rush Job for a company I have no idea of what the price is for non rushed jobs you would have to ask that one.
The better Data Recovery Houses will want a Fee for the quote of around $900.00 with this being taken off the cost of the recovery if it is taken up. But they will give you a fairly good idea of what can be recovered and as you haven't said anything about nasty noises coming out of the actual drive you will most likely be able to recover everything. So you have not totally lost your data but you may not consider it worth recovering.
The other thing that can sometimes be effective is replacing the Circuit Board on the HDD with one from an Identical drive. Sometimes these Circuit Boards fail and just replacing them can recover your Drive but if that works get the Data off as fast as possible and don't trust the drive to be a long term working unit. When something fails on 1 HDD it should be considered as shot and only run to recover your data nothing more. The other thing that can happen is that if the Circuit Board is no longer working there could have been a failure inside the drive and replacing the Circuit Board will result in the destruction of the New Circuit Board so it's a Gamble.
But no matter what [b]Do Not Run The Drive Unnecessarily[/b] as the likelihood of being able to recover your data is decreased with the longer that you run the drive.
Just one other thing here these External Drives are not for full time use they are only for Interment use as they generate heat and in a plastic Enclosure this is not disputed so the drive runs hotter than it should and as result has a shorter life. If you only run the External Drives to Backup or Copy Data back to the computer they will last a long time but if you leave them running all the time they will fail and take your data with them. While it is possible to recover from this it's not cheap.
Col