Strange Search Behaviour

The Ajax search shows only a few results. The results are displayed in a certain order (newest; page order …); Your search term is on a page that is older than the pages shown.
The number – how many results are displayed – is set to 5 by default in Enfold. This makes sense for the normal placement at the top inside main menu. Where you have the search, you might want to increase this a little.

Incidentally, if you only want to display pages (or posts) there, you could also restrict this to these post types.

Put this to your child-theme functions.php :

function avf_modify_ajax_search_query($search_parameters){
  parse_str($search_parameters, $params);
  $params['numberposts'] = 10;
  $search_parameters = http_build_query($params);
  return $search_parameters;
}
add_filter('avf_ajax_search_query', 'avf_modify_ajax_search_query', 10, 1);