For what it's worth, I'd purchased a 2TB Seagate Freeagent Desktop drive a couple of years ago at a pretty good price. I immediately got the problem with automatic ejections. I tried Seagate's recommendations and fixes all to no avail. I tried the device on a variety of different Macs with no luck. I could get it to stay connected if I ran a Windows OS under Parallels and logically connected the USB port from the drive straight through to Windows.
Anyway, I finally gave up on the stupid box and stuck it in a drawer as a hopeless case. A couple of weeks ago, I'd upgraded my iMac to Mavericks and thought I'd give it a try again when I happened to notice it sitting there gathering dust. Of course, it didn't work; still the same auto-eject business. BTW, I'd killed off the Seagate drive kext by this time.
So, I finally just took the internal Seagate Barracuda LP drive out of the enclosure and popped it into a StarTech.com naked drive dock that I have. No problems. As PlotinusVeritas says, it's not the drive, it's the electronics inside the box. I had an old enclosure for 3.5 ATA drives, so I'll have to get one for SATA. No biggy.
The question in my mind is if Seagate must be aware that their sleep-mode electronics is and has been incompatible with Macs for this long, why don't they just fix it? There must be something wrong with the marketing team in that company since I can't believe that the engineers haven't spoken internally about the real source of the problem.
Anyway, now I have a functional Seagate drive... It's just in another company's box.