Hi,
The default WordPress ajax handler cannot be accessed on your site. If you check this URL, it should print out simply a ‘0’ character – that would mean it works. This needs to be accessible for everyone in order for the WordPress ajax requests to work.
Usually, the cause is a .htaccess rule, that is incorrect, but it can be an incorrect file permission as well. Please check your .htaccess file for the rules, as well as any firewall/security restrictions, so that the file can be accessed, otherwise WordPress cannot work correctly.