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With the drive plugged in, right-click the start menu button and select Disk Management.
Does the drive appear there?
It's possible you could have a bad cable if it's sometimes visible, sometimes not. Check this out:
What happens if you plug the drive into another computer?
Is it recognized, and stays that way?
If it's stable when plugged in to another PC then we've eliminated the drive and cable as the source of the problem
and your PC is where to look next.