This has nothing to do with any firmware issue; it is just a loose cable connection. I can say it because, right now I am testing a drive (USB 3.0, My Passport Essential, 1TB) that a colleague bought recently, who faced this issue of the drive getting disconnected recurringly.
When I connect the drive to my office Desktop (which only has USB 2.0 slots and NO USB 3.0 slot), the drive disconnects in about 5 minutes. But when I turn the drive upside down (face down) thereby making the cable contact better, it remains connected. I tested it for 30 minutes twice, and both the times it says on. At the moment, I am trying to figure out a position in which the drive, in its face up position, will remain connected.
UPDATE I: THe drive is now alive after 30 minutes in the face-up (normal) position. All I did was to push the USB 3.0 cable so that it connects well. (I know this is kind of brainless, brute-force technique, but for the time being it seems to work). At least, I hope that that kind of soft-shoving helped. The drive is still alive and connected after 30 minutes.
UPDATE II: There is another possible way to solve this problem. As you may have noticed, the USB 3.0 cable does not fit tight but fits wobbly and it can move up and down a bit. If one slides a small piece of thick paper under the cable (at the gap that the cable leaves with the wall of the drive, due ot its not fitting snugly; a well-fit cable will not leave any such space under it), thus fitting it snugly, the drive does not disappear. I am trying this for about 50 minutes now, and the results seem optimistic.