You've already done a lot of investigative work, here's two more suggestions: Did you take a look at the core file with gdb? Even if it dies in different places, this might reveal a pattern. Also, is memory usage of the child growing over time?

Also, you might want to capture all web input of a child until a crash, dump it and replay it. The problem should be reproducable then. Oh, and you were running Apache with just a single child, right?