Do you have a url where I can see the problem? That might help me determine what is causing it.
I may have to look at the associated code as well. Are there any other session variables you are using that are stored outside of the shopping cart that might not be passed to the https server? The only issue with moving to an https server with a different domain is that session variables are lost. The code we have written will allow you to pass the cart session variables through a form post, but any additional session variables may have to be added manually. Most likely that is the issue, but I would like to take a look.