I had this same problem yesterday. It seemed to be something to do with my Playstation itself rather than the beta application, as I also couldn't access the Store or any of my other downloaded titles, even though my system seemed to be connected. After an hour or so of fiddling with the connection settings, I eventually just gave up. When I came back a couple hours later, everything worked fine.

I don't know if this is related to that issue or not, but I also get "System Error 20019" now when I try to patch the game, so I still haven't been able to log in and begin playing yet.