Hi madvic,
If you enable WP_DEBUG the plugin will log verbose output to the error log. I suggest adding these lines to your wp-config.php:
define( 'WP_DEBUG_DISPLAY', false );
define( 'WP_DEBUG', true );
This should give you an idea about what’s going on. You can read more about wp-debug here.
If the scan can’t finish in 60 seconds it will get killed and run on a wp-cron. So if your wp-cron isn’t functioning that could cause it to hang. You can use WP Crontrol to see the status of the cron. The cron PHP Compatibility Checker creates is called “wpephpcompat_start_test_cron”.
Please let me know what you find!