I don't have a specific answer for you. Unfortunately, per Facebook's (and other social network) guidelines, we aren't supposed to automatically make requests on behalf of the user unless they are active on the site. There could be exceptions to this if we're just keeping them logged in (we don't actually have to make requests to Facebook if we were to implement a "Remember Me" type functionality).
However, how would you expect this to be presented to the user? Right now, when the user logs in with Facebook, they hit that button and authenticate. There isn't a way to associate a "Remember me" checkbox with that authentication.. so there's no way for the user to choose if they should remain logged in. It would be a big security issue if we left all users logged in, so I don't know of a way that meets your desire of keeping social users logged in, but doesn't cause other major issues.
If you have feedback or suggestions, I'm completely open to how this should work and how to indicate to the user that they will remain logged in even if they close their browser.
Thanks,
Alex