I'm having a similar issue trying to integrate your widget onto my client's WordPress page. I created a FB app and tested the Site URL to make sure it's correct, I'm using the numeric FB user id because those seem to work better, and I've renewed the cache and the access token many times, but the API status still says Not Connected (clicking the Access Token button shows no error message but just refreshes the page). In addition, any time I try to visit the Site URL it redirects me to the WP Dashboard if I'm logged into FB, and a FB Login page that then takes me to the WP Dashboard if I'm not.
The client's site is at http://project20something.com, any thoughts on what the problem might be? Deactiving the RFB widget fixes the redirect problem (I've left it deactivated so the site can be accessed without a FB login; the RFB widget is supposed to go where the Twitter Widget is currently).
Thanks for the great widget and the support.