We encountered a similar problem with Internet Explorer 11 where the session cookie went missing after a redirect over https.
The request chain looked something like this:
initial request to / -> session cookie set -> redirect to an external URL -> redirect back (session cookie lost)
Our problem was due to an invalid host name according to RFC952, we had underscores in our test server URL. It seems that Internet Explorer silently drops the session cookie on redirect over https if the URL does not conform to RFC952. When using dashes instead of underscores, everything worked as expected.
The original solution was found in the Update 2 section of this asp.net blogpost from 2004. Related microsoft bug ticket here.
Hopefully this will help someone.