When you put a Drupal site into maintenance mode, it actually is serving a custom error page. By default, Nginx is handling the error pages. If you want Drupal to do so, edit the file /etc/nginx/sites-enabled/drupal and comment out the following:

#  error_page 404 /404.html;
#  error_page 500 502 503 504 /50x.html;
#  location = /50x.html {
#      root /usr/share/nginx/html;
#  }

Finally, restart Nginx with sudo service nginx restart