Seems that is not possible to send requests to the proofreading service from your site.
May be a limitation on your server configuration, a firewall or something similar.
We made some test in the last days. Your problem can be reproduced disabling fsockopen php function or cURL library from web server.
Please make sure you have enabled it on your apache/nginx server configuration.
It ended up working although I did not modify settings. It might be a clash with iThemes Security as I was also facing bizarre behavious when trying to create pop-ups with javascript code created by MailChimp.