Every 15 minutes sounds like a timed task. Check the crontabs first to see if there is anything that may be causing this.
Software itself could be the issue as well. You may want to consider reinstalling the httpd.
Memory comes to mind, but 15 minutes on the dot doesn't sound like a memory issue to me.
Stacked with the other post you have for connections not closing, I'm leaning towards software. I'd start by patching it up to the highest level they have, and if that doesn't work, I'd reinstall and see what the results in.
And of course make sure you check the error logs to see if there is anything useful in there.
header('HTTP/1.1 420 Enhance Your Calm');