The AJAX fields can field to load if there is a JavaScript error or there is a PHP error during the AJAX request. You need to look for JavaScript errors and turn on debugging and logging and check the error log to see if there are any php errors during the request. https://codex.wordpress.org/WP_DEBUG. If both of these are negative then I’d go back to the internet connectivity assumption, especially if the site works fine for me and only breaks for the client.
