Well, the current project I'm working on is using the Zend Framework on the server side. When I login, a Zend_Session is created and stored on the server in much the same way it would be with a standard PHP website. Each post from the Flex app to Zend_AMF would check for a current session and then respond accordingly.
Of course, the client app could handle ALL of the session processing, but from my security-minded view, only the server can safely and securely handle the login sessions and know if the client is logged in or not.
If the client were to handle it's own login validation and then the server just assume that if the client says it's allowed to perform an operation, just do it....well, it would be too easy for a client to be spoofed and cause a security hole in the entire process.
Of course, if you are not using a server-side database/system, and only using a local database then everything I just said can be deemed irrelevant.