"Site off-line due to technical problems" (no extra info in message). What causes this? What causes the following message on a Drupal 6 site with no other information?

Site off-line
The site is currently not available due to technical problems. Please try again later. Thank you for your understanding.
If you are the maintainer of this site, please check your database settings in the settings.php file and ensure that your hosting provider's database server is running. For more help, see the handbook, or contact your hosting provider.

I think it means that the database did not respond in time but can someone confirm that?
I can force almost the same message by stopping the db but then it has some extra info under it about not able to connect to the db. That makes me wonder what it means when there is no extra info at all.
It is definitely related to slowness. It happens sometimes when the site is very busy and therefore slow. There is no obvious reason recorded in either the Drupal or Apache logs
Thanks
I'd wager you're using Drupal 6. And yes, it means a fatal error in connecting to the database.