Here's an idea, modify your apache conf to emit Etag header (it should do it by default),
and then modify your conf to log the Etag sent
%...{Etag}o:,
so when you get a blank white page,
you can look at the http headers (Live HTTP Headers :: Firefox Add-ons),
and then look for that Etag/ip combo in your apache logs.
Thanks everyone for the advise. I'm going to try these things out and will post the outcome in the next couple of days. Unfortunately, this isn't my day job. I can only do this in my free time :)