Hi!
There is an error message which appears every time any of the plugins try to update:
[html]Warning: array_merge(): Argument #2 is not an array in /home/armoniea/public_html/modaceramica.it/wp-includes/load.php on line 63[/html]
To test this, I have disabled Ajax Search Pro, and tried to update another plugin, and the error message is still there, please see the screenshot: https://i.imgur.com/YdTSRLy.png
This means that the error is not related to this plugin unfortunately.
However this does not seem like a serious issue, I recommend turning off the debug mode in the wp-config.php file first, that should get rid off that error message:
[php]define(‘WP_DEBUG’, false);[/php]
The error is definitely not caused by this plugin, but because it is outputted everywhere, the ajax requests are failing. For safety reasons, you should try the manual update instead.