Hi,
As long as nothing is stored in the session, the session id will change again and again. Each user session have its own set of session variables.
That said authentication is already handled by ASP.NET so User.Identity.Name would give the user name and storing a password for the whole duration of a session doesn't seems to make sense (it is best for small, user scoped data you'll use very frequently so not for a user name which is already provided when using ASP.NET built in authentication or for a password that seems usefull only at log time).
For now my understanding is that session variable are not set. If I remember some browsers are not handling creating a session and redirecting (creating a session returns a cookie while redirect tells to go to another page so if you set a cookie and redirect at the same time, the cookie might be not carried over to the next page). What is your browser?
Ah: found https://support.microsoft.com/en-us/kb/176113 it would actually depend on your web server. Do you still use IIS6 ?