This is related to session cookies. Your main page works on another domain than your embedded shop page. Thus, the browser cannot store cookies from the domain where the shop is running. Cookies are always stored domain-dependent. If you would run both systems on one domain, it would work.
Edit History
Normal behavior. This is related to session cookies. Your main page works on another domain than your embedded shop page. Thus, the browser cannot store cookies from the domain where the shop is running. Cookies are always stored domain-dependent. If you would run both systems on one domain, it would work.