It has to do with the number of requests plus the number of allowed processes plus the requests each process was allowed to serve. At a limit of 300 requests per process, the processes fell over at about 3 seconds time. With only 20 processes, dying every three seconds, the server was overwhelmed. So it's really a combination of issues.

Looking at the records for MySQL data, there wasn't that much of an issue there with MySQL connections. This is probably due to the fact that the page cache was working correctly.