Julian, thanks for your reply. It's clear though that my site isn't the only one affected. I know of at least five other DH users (inpassing.org, linkstew.org, unreliablenarrator.com, etc.) who are having the same problem, and it's clear that the mysql server is being flooded.
The problem is not with my, or their, PHP code. The problem (and the solution) shouldn't be a mystery, since this is the Nth time this has happened in the last month.
This is completely unacceptable, not the least of reasons why being that, when the service of hundreds of your customers is completely disrupted, it takes 14 hours to get an email response back that basically says, "Oh, yeah. Something's wrong. I don't know what, but I'll have someone check on that for yah. It's probably just you though."
This is an insult to all your customers, whether they voice it as loudly as me or not.