Mountain Lion/Mac Mini 2013 randomly ejects external hard drives

My wife bought me a 2013 Mac Mini for my birthday a few days ago to replace our 2010 Mac Mini as our home theatre hub. I have never been more disappointed in an Apple product in my life.

The new Mac Mini (running Mountain Lion 10.8.3) is constantly ejecting my external hard drives without warning. I've read about the issue from other people who are just as frustrated as I am, and it seems there's no solution.

I have a total of six external HDs connected to the Mini via USB 2.0 cables at all times:

Vantec Nexstar MX 2 enclosure: 2 x Western Digital Caviar Green drives ranging in size from 2TB to 3TB

Icy Dock MB561US-4SB-1 enclosure: 4 x Western Digital Caviar Green drives ranging in size from 2TB to 3TB

Note that these enclosures have their own power supplies. I can't make it more than an hour without at least one of the drives randomly ejecting. I'm worried that these random ejects are going to corrupt valuable data.

People have variously suggested it could be Mountain Lion 10.8.3, or the Mac Mini's hardware, or my USB cables, or the hard drive enclosures, or the drives themselves, or the Energy Saver settings, or maybe even the drivers for the enclosures or hard drives. I've tried every solution suggested here with no success: https://discussions.apple.com/thread/4250547?start=0&tstart=0

What I can say for certain is that this is the same setup I've used for the last two years on my 2010 Mac Mini running OS X 10.6.8, and that computer has never randomly ejected a drive. Ever.

Does anyone have a magic bullet solution? I'm ready to walk the shiny new Mac Mini back to the store.