Logged in status does not change despite logging in user into the site

I am going to find it a little difficult to describe the problem - but let me try.

website: usagoshopping.com

-User A logs into the site the first time using facebook
- The user is logged in and redirected to the page set up for logins.
- User logs out

No problem so far

- User A logs in the next time
- Login status on the page does not change, and he is not redirected
- Page refresh/clear history however shows that he is logged into the site
- The logged in status with user greeting does not show on several pages - but refreshing updates the status
- similarly logging out - logs out the user - but the 'Hello User' message continues to show. Refreshing the page shows that the user is logged out

My conclusion is that the 'Registering the user', logging in and logging out functions happen fine. However the login status updates do not update.
Thats about the best I can explain the problem.

Kindly help. If you need the admin login - do let me know (the credentials haven't changed from last time)