I'm not sure if you know this, but with WP_DEBUG enabled, it's showing the following NOTICE level error in the administration settings page for this plugin:
Notice: Undefined index: url in /var/www/wordpress/wp-content/plugins/json-api/singletons/api.php on line 174
I hope that helps.
Thank you very much for your hard work on this plug-in by the way! It is just what I needed to interface a plug-in I'm writing so data can be retrieved by other WordPress sites.