I am having same problems. Late i7, 27" Mac 3T Fusion Drive, 16gb RAM. It just auto un-mounts w/ same "ejection" error message. I've seen some discussion of possible iTunes (corrupt file) related conflicts. (I rebuilt iTunes, reinstalled all my apps on my ios device. That seemed to help a small bit (perhaps bc iTunes is accessing 1000s of files at a time?? USB conflict? SATA card conflict?)
Repairing and running DiskUtility/ permissions had virtually no long-term benefit -- even when done from a different boot drive.
Then I found this entry that Mavericks introduced a USB driver conflict that may affect HDs -- especially when copying/moving over 500 files (i.e. TimeMachine, running itunes or another HD cloning app. Mine wd crash when I was running SuperDuper-- which normally works great.)
See this discussion: <http://www.enttec.com/support-center/kb/article/108-OS_X_Mavericks_(10.9)_-_IMPO RTANT> and
<http://www.dpreview.com/forums/thread/3605926> discussion of the problem.
I have also unmounted and unplugged my ext USB HD (used for backup-- but now have no way to clone my HDs.) I also disbaled the HD sleep function. That seemed to help so far. (Fingers crossed.)
Also, copying more than 500 files at a time seemed to create the crash (like if you were backing up your drives to an external USB connected drive.) Frustrating. Howver, this thread has been really helpful.
Please report back if you found a solution / fix. Thanks.
(Mac user since the original 512K, 1983.)