We've been in beta for pretty long, how far are we from maturing into a full site? How do we move towards it? And who is the governing authority that determines if a site should progress or not?
The StackExchange community team decides when to promote or shut down a beta.
Robert Cartaino has written about the graduation requirements a few times, but the basic gist is that it's mostly subjective. The only hard requirements I've seen repeatedly mentioned are the duration (over 90 days) and the number of closers and editors, all of which we technically meet.
However, looking at some of the other sites in beta, I would suspect the SE team is still waiting to see if the traffic and activity on this site will pick up more before they graduate us. Sites like the Personal Finance beta are in a much healthier state, yet also haven't been graduated (though I think they are close).
I think this overview might give you some idea of why the SE team hasn't graduated the site yet: