Firstly, you could deactivate automatic updating. This will stop it from happening at all. To do this, you would have to enter the following in the functions.php of your child theme or via a code snippet:
// Disable core update emails
add_filter( 'auto_core_update_send_email', '__return_false' );
// Disable plugin update emails
add_filter( 'auto_plugin_update_send_email', '__return_false' );
// Disable theme update emails
add_filter( 'auto_theme_update_send_email', '__return_false' );
Alternatively, there are also some plugins that can be used to control this:
https://wordpress.org/plugins/tags/updates/
However, you must then remember to update the plugins yourself at regular intervals. This is because some updates contain security fixes that are also relevant for your websites.
Now, of course, it is also questionable why updating does not work. Take a closer look at the message. Is it possibly a Pro plugin for which the licence is missing? Or is there a problem with PHP compatibility? Something else? Depending on what it is, you should also look into this as it indicates a problem with your website.
