Jonathon,
I hear what you are saying about a coding error. But here is where I am left scratching my head.
The day before we made this account upgrade, all of my WordPress sites were running on WP 3.5.1. Most of them were configured alike, using the same plug-ins. And all of them were running smoothly, all day, every day.
The day of the account upgrade, with no changes being made to any of them, the WP sites started displaying extremely slow load times and started showing the above error, every day. When I say no changes were made, I mean all the sites were still running WP 3.5.1, with all of the same plug-ins.
How can a coding error come into play, when none of the code was changed?
It was suggested a couple of the plug-ins were out-dated and causing the problem, so I upgraded them, only to see the same results.
It was suggested one or more of the plug-ins was simply incompatible with the others (even though the alleged incompatibility had never manifested itself prior to the upgrade), so I disabled all of the plug-ins, only to see the same results. I started adding plug-ins, one at a time, only to see the same results. I switched to the standard WP theme, thinking Thesis might be causing the problems, only to see the same results.
I am aware WP can be a little awkward with the removal of plug-ins, so in early-June, I wiped one of my WP sites clean. I deleted all of the site files, deleted the database and started with a fresh installation. Only to see the same results.
When WP 3.5.2 was released in late-June, I upgraded to it, in the hope I would be rid of the problem. So there was a code change made at that time, but all of the sites continue to load slowly and crashing, every day.
I set up another test WP site, using zero plug-ins, only to see the same results.
Very early, on the morning of 4 August, I upgraded one site to WP 3.6. I successfully ran the upgrade script and when trying to access the control panel, after the software upgrade, the site crashed. Approximately 4 hours later, it was back up and running, with no changes made on this end.
Yes, I agree the error seems to indicate some kind of a coding problem. But I am not talking about a piece of custom software, written with questionable coding, I am talking about bog-standard WordPress. How many millions of sites use the same code, with zero problems? Which ultimately brings me right back to what I said, earlier - The day before we made this account upgrade, all of my WordPress sites were running on WP 3.5.1. Most of them were configured alike, using the same plug-ins. And all of them were running smoothly, all day, every day.
All I know to do is to apply top-down logic to all of this. The result to that makes no sense, but when there were no other changes made, what else can it be?