I have the Mac Mini back again.
They phoned me and asked permission to do a clean install on it again. I gave permission, so what I got back was pretty much what I had given them as I had already done one clean install.
Then it came back. They had run all their tests and found nothing wrong. They said it was probably the Drobo that was causing the problem.
I brought it home, plugged it all in and promptly got kernel panics. So I sat back and thought about it.
The Mac Mini had problems before I got the Drobo. Since then, they have replaced the motherboard. Let's experiment. I disconnected the Drobo, removed Drobo software, turned off iTunes (which depends on the Drobo for its material), and left it. I would have expected a kernel panic or two within a day, but got nothing. It was rock steady. I used it for browsing, updating software, fiddling about, but no Drobo. Rock steady - no kernel panics, no problems. So I would guess that the replaced motherboard fixed the original problems I had.
I plugged in the Drobo, installed the Drobo software and left it. I did not start iTunes. Within a day, I noticed a notification that the Drobo had been ejected improperly, and the Drobo was not showing on the desktop. It was still plugged in, but it was not accessible. Now that was interesting. I had to reboot to get it accessible again. I left the Drobo connected again, and again within a day, I had a notification about improper ejection and the Drobo was not showing and not accessible.
Doug suggested it might be the USB 3 cable, so I used a cable that I knew was good. Same problem occurred. I told the Drobo not to spin down the drives. Same problem. I told the Mac Mini not to spin down the drives to save power. Same problem. Now we're getting somewhere. Without the Drobo, the Mac Mini stays up and functions as expected. With the Drobo attached, I am getting problems. Looks like Apple was right when they suggested that the Drobo was the problem.
I tried an experimented. I rebooted, got the Drobo active, and fired up iTunes. After a day, the Drobo got ejected and the system shut down with a kernel panic. So when iTunes is relying on a drive that gets ejected, it cannot handle this and the system shuts down with a kernel panic. Okay, I agree that the drive should not get improperly ejected, but iTunes shouldn't be that touchy.
I used Google and started searching for this problem. Oh look, I am not alone. This is a common problem. It appears that either the Drobo has implemented USB 3 badly, or Apple has implemented USB 3 badly, or they both have small variations. But Drobos are getting improperly ejected by Macs a lot. And there is no fix.