enqueue script only if it is not already enqueue

The WordPress enqueue system should prevent the inclusion of the same script multiple times, and does when I test it. For example, the following enqueues a Core script and echos a counter. If I put this shortcode into a post 4 times, I get “0123” but the media script only loads one time. The same test works with several other scripts I tried.

function my_shortcode( $atts, $content = null ) {
    extract(shortcode_atts(array(
            'title'  => '',
           ), $atts));
    static $counter = 0;
    echo $counter++;
    wp_enqueue_script('wp-mediaelement'); 

}
add_shortcode('enq','my_shortcode');

If you are getting the same script loaded over and over, there is a problem with your site, but I am not sure where start guessing at what.