It is highly likely that the browser is not sending the authentication cookie from the first site to the second site. Check the cookie path and the domain. Both sites must be on the same domain, and the cookie path must be set to a common root.
See this link for more details: Cookie Domains and Paths
To aid in troubleshooting, use a utility such as Fiddler or Firebug to view the cookies being sent in the request, and verify that the authentication cookie set by site 1 (where the user logged in) is also being sent to site 2.
If the sites aren't on the same server, also check if they are using the same machineKey configuration.