TLS keep-alive

[Will]

Hi!

I'm accessing my app using a WinINet client using INTERNET_FLAG_KEEP_CONNECTION.  When using HTTP the keep-alive works perfectly and requests stay under one TCP session, but when I switch to HTTPS (INTERNET_FLAG_SECURE on port 443) then for every request I am getting a new TCP and TLS session (Client Hello, Server Hello, etc etc) for each request.  Is there any way of getting keep-alive to work under TLS?  Is there something I'm doing wrong?  Is this likely a problem with WinINet or App Engine?

Cheers

Will