IE9 & Drupal Form with in iFrame
This looks like a security problem to me.  I examined the headers being sent by IE and the session variable in the cookie doesn't appear to be getting set/transmitted.  This is because IE has strict rules about cookies in iFrames, whereas Firefox does not.  Without the session variable, your cart is not being saved.  I would take a look at this related question: https://stackoverflow.com/questions/389456/cookie-blocked-not-saved-in-iframe-in-internet-explorer and apply the solution presented there.  It should solve your problem.