Hey Jeffrey. I have confirmed that turning off the 404 logging makes the problem go away.
Here is the exact issue the sys admin reported. He has it narrowed down to this plugin:
The SEO Ultimate plugin is having trouble with a 404, and the error message is so huge, the plugin could not save it's value into the WP database. So, instead that 404 error from SEO, turned into an error in PHP, so it's logging it to its logfile (php53_error.log). And that is happening *very* frequently.
The SEO plugin has a setting for handling 404's and different types of them. Omar has unchecked a few options in the hopes that it will subside the types of errors causing the logs to fill up. I have no idea what the result will be.
THE DIFFICULT QUESTION - What is SEO Ultimate trying to save to the database that is so huge. Looking at the php error log, it looks like SEO saves it's own log to the database and it got so huge, it won't work.