The drive may unmount and remount for various reasons.
- power starvation is the most common but in your case, it doesn't seem to apply
- data link reset is another possible cause. It could apply to you. If a read or write fails, due to a defect in the disk (or the controller) the system will retry a few times and if the error remains it resets the data (SCSI/SATA) link. At that moment the USB link is reset and the mount becomes stale. Then the device comes back on line and a "new" USB device is discovered (and mounted elsewhere.)
If you experience link resets when reading or writing, you should see traces in /var/log/syslog. In general when you get link resets and all cables are properly connected, it means your HDD is dying of old age. So you may want to check how your HDD behaves when you connect it to another computer and write heavily to it.
Then there is a possibility the USB-SATA bridge doesn't work as expected under linux, or the driver requires some options. I think this is harder to debug, so it's better to check that the HDD is ok first.
"S'il n'y a pas de solution, c'est qu'il n'y a pas de problème." Les Shadoks, J. Rouxel