The MYSQL wait_timeout setting value needs to be increased.

The Site Studio rebuild can be a long running process, depending on the amount of content and complexity of your website. 

In some cases a large or complex website can trigger this error "MySQL server has gone away” after or during the process. If your website encounters this error, please follow this user guide on How to override the default MySQL wait_timeout setting. Once the wait timeout setting has been increased re-run the rebuild process and the error should no longer occur.

interactive_timeout; as per the instructions found here, update the database configuration in your settings.php as below:

$databases['default']['default']['init_commands'] = array(
  'wait_timeout' => 'SET SESSION wait_timeout=1200',
  'interactive_timeout' => 'SET SESSION interactive_timeout=1200',
);