FWIW, I am having the same issue. I connected an external HD that had been connected to a windows machine without issue and it started to disconnect as soon as I connected it to the mac. I tried changing cables, but that didn't work. One powered USB port did work, however the copy time was going to be 3 days (250gb of files). Another Powered USB port produced the dreaded eject issue.
So I pulled the drive out of its enclosure and connected it using a SATA to USB adapter. First time out, it wouldn't read, the second time it read but ejected.
Finally, I tried something else. The disk has 2 partitions, one containing the files, the second containing a backup of my PS3. I ejected the partition containing the ps3 backup, leaving the one I need mounted. So far, 50gig of files copied with no ejecting.
I haven't seen a whole lot of discussion on this thread around the format of the drives. In my case, both partitions are formatted with NTFS.
I should also mention that when the drive was in the enclosure, NTFS-3g would show an error something to the effect of the drive didn't respond within 15 seconds and was going to be ejected. That problem disappeared when I pulled the drive out of the enclosure.
So, multiple partitions formatted with NTFS perhaps an issue? I have 2 other drives connected to the same computer via a dock, both Mac formatted, and no issues at all.
53 gig copied and counting...???