1. So hard drive doesn't work properly no matter in what position it is?
2. When you power on the hard drive,does it start spinning and then after short amount of time it stops spinning?
3. When (like you said) hard drive after few minutes disappears,do you hear that WINDOWS DISCONNECT sound EVERY time when that happens or not?Because that usually leads to a bad power wire connection if it's not connected properly even though it LOOKS like it's connected properly.
4. When (like you said) hard drive after few minutes disappears,in that moment do you hear ANY sound from the hard drive like it does not have enough power?Because that usually leads to a bad power wire connection if it's not connected properly even though it LOOKS like it's connected properly.
5. Also if your hard drive is SATA,make sure you do NOT use this type of power SATA wire:
I am talking about this black part.That one is bad quality and wires inside of it move very easily and that can result in a broke power connection to the hard drive and for that reason your hard drive does not have enough power in a certain moment and that results in your hard drive disappearing.
Use this one instead:
6. Do you use this kind of external power supply for your hard drive?
As you can see this one ends with PATA POWER wire and you just plug the SATA power wire to it and then to a hard drive.Is that how you power it up?
7. Did you try what Johnb35 suggested by connecting the hard drive directly to your computer's power supply (for power) and to your SATA port directly on the motherboard (for data)?
8. Does your USB port (the one you are connecting your hard drive to) work properly?
9. Is your USB port (the one you are connecting your hard drive to) clean?Because dirty USB ports can result in a bad connection and are also sensitive even on the smallest wire movements and can result in a lost connection.
10. Did you try to use some other external operating system which you can just load directly from the CD-ROM disk like Linux Ubuntu and see if the hard drive disappears there too?
11. Any messages from S.M.A.R.T. ?
So...you said that when you connect the hard drive you can see the data and go through it.That shows that hard drive still works.So answer on above questions and we will see what to do next.
Cheers!