I purchased the Belkin 4-port USB3 hub that is sold at the Apple store. Since making this change, I have not experienced the problem again. I have literally put my iMac to sleep *many* times just to prove that the problem is really solved. Now, when it goes to sleep, the hub and drives shut down, as expected (all of the lights on the hub shut off). When the iMac returns from sleep, the hub reactivates (all the lights turn back on) a moment before the iMac comes back to life, and the hard drives are visible and ready to use. I have had no further disconnect messages.
Have you run into the situation where the Belkin hub seems to get into a wake/sleep cycle that gives the Mac insomnia?
I have 10.8.4 on a rMBP that seems to cycle (sometimes, sometimes well behaved). It doesn't wake up the whole way, but is maintenance wakeup that also wakes up my third party display (TB-DP connection). System logs says hub port 2 is waking up, which is a recent OWC USB3 raid.. but I can turn off that Raid and sometimes the rMBP gets into the same cycle regardless. Blue Tooth is turned off. I may try swapping cables.