That message is being posted by JFBConnect when we detect a server configuration error on your site with IPv6. After that message is displayed, JFBConnect falls back to try and use an IPv4 connection, which should work. I'm confused that you can't register at all; it should honestly just take an extra second to try the IPv6 and then fallback to IPv4.
As for the underlying issue, do you know if there were any server changes recently by your host? IPv6 is very tricky to setup, and we've had many cases of partial implementations where DNS lookups are IPv6, but the actual outbound requests don't work, or cURL is not configured for IPv6.. or vice versa and a lot of other partial, bad configurations. You may need to contact your host to understand what's changed to break the behavior.
Finally, if you get it working, the message can be hidden by simply disabling the "Display Facebook API Errors on Front-End" setting. There will still be the minimal delay for trying IPv6 first and then falling back, but your users shouldn't notice any difference.
Hope that helps, but if you need anything else, just let us know,
Alex