When you say "log files" do mean access logs, error logs or both? Are any true errors (500-level) being generated?
You could set your error logs to debug level-- but this gets recursive, since the extra logging itself would create more activity :(
Could it be something embarrassingly obvious like an unintended chain of rewrites (what Apache calls "internal redirect")-- not enough to trigger a shutdown, but enough that an ordinary request generates 5 times as much activity as it ought to? This won't show up in regular logs.
I assume you've eliminated the predictable explanations, like any changes you might have made right before the spikes started. Including, of course, the changes you didn't bother to consider because they can't possibly have any connection with the current problem ;)