So I had a similar problem. It would eject randomly. Sometimes after 2 mins, and eventually almost immediately after hooking up the hard drive. I tried using the Seagate dashboard, but it was useless. Only allowed you to manage social sharing settings.
The first thing I did was run the firmware updater that seagate provides. Its on their downloads page..
It didn't recognize my drive as needing a firmware update. So I got ****** and did what any mac owner would do... Call home.. Apple found the same solution I was seeing in some places. DELETE the seagate backup plus extention. System/Library/Extensions/SeagateBackUpPlus.kext
Restart your mac. See if that helps your eject or restart issues. My guess is it didnt. The next thing I did was run the firmware update again. Plug your hard drive in again. It might take a second to recognize, but the firware updater (1.2.2 I think) will see theres a firmware upgrade needed. I think the extension kept it from seeing that.
Update as quick as you can before the drive ejects... The updater will prompt you to unplug and plug it back in. It should say update successful. The drive will dissapear again, but this time on a safe eject. Reboot the comp, or unplug and plug the drive back in. The drive has been up and running, falling in line with my other drives and rebooting when I want it to.
Hope that helps....If you need more help, my email is on my website www.humbledown.com