If you click it and it starts spinning but never submits this means that there is some error happening during the AJAX process.
Because it was working before does not mean that there is not a problem in another plugin or in the theme. I am running ACF on a site with WP 4.3 and the latest version of Pro with a standard 2014 theme. Everything is working as expected, I’m not seeing any errors and I can publish and update posts.
Turn on debugging in WP, https://codex.wordpress.org/Debugging_in_WordPress, put this in you wp-config.php file
define('WP_DEBUG', true);
define('WP_DEBUG_LOG', true);
define('WP_DEBUG_DISPLAY', false);
try saving a post an then look in the log file to if there are any errors and what they are.
