Just adding to the pile, in the interest of input which might reveal something...
After one year of excellent performance, my 2013 iMac has suddenly exhibited this false(?)-eject behavior. El Capitan 10.11.3. The external HDDs are four 2TB Hitachi in a 4-bay enclosure (OWC Elite pro Qx2) connected via USB 3.0.
If one looks for recent activity that night have triggered this, the one 'unusual' thing I did do, just yesterday, was to update my iPod Touch to iOS 9.2.1, via iTunes on the iMac. But I've done one or two other iOS upgrades in the last year without incident. I try best I can to disable any and all syncing between devices. FWIW, Spotlight is entirely enabled on the Touch, and for the iMac I'm considering the disabling steps discussed in this thread.
Another misbehavior that popped up when the ejects and their warning messages appeared was that iTunes started playing back erratically and/or distorted. (iTunes > BitPerfect > outboard DAC; music files are stored in two of the four ext HDDs.) As of today, accessing the HDD for music (ripping or playback) seems to trigger the eject behavior, for all 4 drives.
Also, the entire system now stalls for several seconds upon Shut Down. I haven't had a chance to try Sleep modes.
I read through most of this thread, and what with all the many various devices, OSs and connections described, I think this points to a hardware / firmware problem on Apple's end.
Furthermore, this issue seems to go back several years. I had to face this a couple years ago on a 2008 iMac Snow Leopard, with the same OWC enclosure / HDDs. In that case, I had the enclosure (only) replaced and it seemed to resolve the problem for a while, but the subsequent ejects were at least infrequent. When this HDD / enclosure migrated to this newer iMac (shipped with Yosemite) the problem went away altogether. Until today.
Which makes me further suspect hardware / firmware. And worry about HDD content damage.
Just for disclosure, I'm an atypical user in that I'm deliberately detached from most convenience apps and syncing:
No USB hub (all connex directly to the iMac)
No Time Machine (don't like it, backups via SuperDuper)
No Spotlight (don't like it, only use command-F)
No iCloud (or any cloud)
No syncing between devices (there is only the iMac and Touch)
WiFi disabled 99.99% of the time (Airport Extreme)
All this in the interest of simplicity and/or security. Which makes the hardware / firmware suspicion grow when I see the ejects happen.
Anyway...
Fortunately, I've got a couple years left on AppleCare (I might need 2 years to resolve this). I will approach them with this. I'm sure they will immediately suspect the 3rd-party drive / enclosure set up (all vendors do this), but I will direct them to this thread, and note there are several others like it. I'd like to hear their input on Spotlight disabling before I actually try it.
If anything insightful comes of it, I'll post back here.