Please, update our theme to the latest version and also all included plugins via Appearance -> Install plugins. Then, disable all external plugins that are not related to our theme and provide us your FTP access so we can investigate the problem.
OK, now we see the problem. When you click on “Update” button it sends a regular AJAX request but your server redirects it to 404 page https://gyazo.com/39dd769f43cd83339046a0e718386f75
It seems to be a problem in your server configuration if it doesn’t work even if all plugins disabled.