periodic ssl read timeout

We do an https POST to a particular windows host several thousand
times each day.  About one out of every 300 requests results in a
server error, which status_line say's is an ssl read timeout.  It is
in fact timing out from what I can tell because it returns right after
180 seconds has passed.  The normal response time on a post is 1.5
seconds.

The windows host we are posting to is a credit card processor called
Vital.  They are the ones that payment gateways like Verisign send
their transactions to.   I'm inclined to think that this is a bug in
libwww, one of the SSL modules, or openssl itself.  One out of 300
transactions is a fairly high failure rate for someone like Vital not
to notice.

So, what is a good way to debug this problem and find the source?  I'm
already using LWP::DebugFile but it doesn't show me anything
interesting.

Chris