This disconnect problem was with me for some time and I've shared quite a bit on how it affected one of two identical drive enclosures. Back then, after extensive testing, it pointed to some firmware issue on some drive enclosures.
Update: Last week I found some corruption deep in the OS files on my MacPro (the machine I was having disconnect problems with) when I was not getting the response I should from Unix Terminal inputs I was working with. While Disk Utility continued to say there was nothing wrong with the partition, my attempts to rebuild the directory with Drive Genius 3 always ended with a failure due to a warning the OS10.8.5 system drive was corrupted. Since I didn't want to do a clean install and reload the tons of programs and updates on my main MacPro Tower, I cloned my laptop (has 10.8.5 with no issues) over to my MacPro since it has most of the programs and would be the least troublesome way to change my OS to a fresher install of 10.8.5 on my MacPro without losing all the organization of files.
After cloning and using the Terminal app to reset all my permissions on my home folder to default (they got screwed up in the cross-over) I was delightfully surprised to see my new DataTale enclosure (the enclosure constantly disconnecting) very stable and working perfectly; both shutting down and waking up from sleep without disconnecting….surprise, surprise. This points to some aspect of the 10.8.5 OS I've been running for years on my MacPro. As to what was wrong and how the change to a fresher 10.8.5 OS fixed the problem, I don't know….sorry.
If you are still having this disk-disconnect problem, I suggest a clean install if possible to fix the problem on many external enclosures. There's something in the system files that doesn't show up on Disk Utility or overtly affect your machine's operation, short of the disconnect issue . I wish I knew what it was, but at least now I'm happy my machine doesn't have this problem anymore and the Terminal app fixed all my permissions on home folder files which was driving me crazy. I realize a clean install will be problematic for many who have lots of software apps installed and the computer organized the way they want it. Apparently from what I've read, one can use the recovery mode to switch out only the system files, which might very well work, but after cloning back and fourth over the years the recovery partition no longer exist on my HD. In it's place I have installed a bare minimum OS Repair partition with all my repair software that I can boot into a anytime to repair the main OS.. I find this so much more convenient than using Apple's recovery system which would take forever and require the internet.
Thanks to all that have contributed to this issue.
Good luck.
Marshall