I do have one suspicion, though: I’ve noticed that when your machine goes to sleep for an extended period, the Drobo also goes to sleep. When the computer wakes up, it does so a lot faster than the Drobo and, as a result, Mac OS X throws up the "Device Disconnected" dialog that you see if you pull a USB drive too soon. That’s not usually a good thing.
Tom indicated to me that a Drobo should not behave this way and that there are two possible causes of this: a fault with the Drobo itself or a problem with one of the drives.
Yesterday, my replacement Drobo arrived. I pulled the drives from the original Drobo and put them into the new one and tried a couple of sleep/wake cycles. The new Drobo behaved just like any other disk - it went to sleep (lights off) when the Mac did, and woke up and reconnected correctly when the Mac woke. As you would expect, the data wasn't accessible until the drive was fully online but that's the same as any other external drive.
So, in summary, lessons learned, problem solved, Drobo replaced and Fraser happy. The Data Robotics team worked hard to make a bad situation right, and I thank them for that.