Execute shortcode twice in the same page

Question

I believe the real issue you had was with echoing your data instead of returning it.

A shortcode should return the output to be drawn, which is then drawn in place of the short code.

Here is the code using HEREDOC syntax for outputs and the query. I believe this makes things much more readable once you get used to it. See http://php.net/manual/en/language.types.string.php#language.types.string.syntax.heredoc

Changes to get_past_events:

Moved it out of the other function (for clarity)
Provided a default input variable (for clarity of input expectations)
Skip processing if no events received
Moved get_site_url() call out of loop (same for every item)
Used HEREDOC notation (for clarity and clean output)
Renamed the function to make it less likely to conflict

The get_past_events function:

function do_my_get_past_events( $past_events = array() ) {
   $output="";

   if ( is_array($past_events) && 0 < count($past_events) ) {
      $site_url = get_site_url();
      foreach ( $past_events as $past_event_slug ) {
         $output .= <<<HTML
<li><a href="https://wordpress.stackexchange.com/questions/175004/{$site_url}/eventi/{$past_event_slug}">{$past_event_slug}</a></li>

HTML;

      }
   }
   return $output;
}

Changes to archive_render:

Pull shortcode attributes into an array (clarity)
Declare event_items (so we can skip processing if needed)
Added prepare statement (prevent sql injection) using digit
Used HEREDOC for query string (clarity)
Adjusted rientro variable (left hand declaration – clarity)
Changed string variable to custom_short_code (clarity)
Return the final output (the actual fix)
Added optional block in case a default is wanted
Renamed the function to make it less likely to conflict with anything

The archive_render function:

add_shortcode("archive", "do_my_custom_archive_render");
function do_my_custom_archive_render($atts) {

   $options = shortcode_atts(
      array(
         'year' => 0,
         'rientro' => 'no'
      ),
      $atts
   );

   $past_event_items="";

   if ( !empty( $options['year'] ) ) {
      global $wpdb;

      $query = <<<SQL
 SELECT event_name 
 FROM wp_em_events 
 WHERE 
   EXTRACT(YEAR FROM event_end_date) = %d 
   AND event_end_date < CURDATE()
SQL;

      $query = $wpdb->prepare( $query, (int) $options['year'] );

      $past_events = $wpdb->get_col($query);

      $past_event_items = do_my_get_past_events( $past_events );
   }

   $rientro = ( 'si' == "{$options['rientro']}" )? 'yes' : 'no';

   # If there are no event items for the year provided the user will get an empty box
   # If that is not what is wanted, uncomment the following 3 lines
   # if ( empty($past_event_items) ) {
   #    $past_event_items="<li>No Events Found</li>";
   # }

   $custom_short_code = <<<HTML
[one_third last="{$rientro}" class="" id=""]
   [accordian class="" id=""]
      [toggle title="{$options['year']}" open="no"]
         <ul>
            {$past_event_items}
         </ul>
      [/toggle]
   [/accordian]
[/one_third]
HTML;

   return do_shortcode( $custom_short_code );
}

Here is the same code without using HEREDOC for those unfamiliar with it.

function do_my_get_past_events( $past_events = array() ) {
   $output="";

   if ( is_array($past_events) && 0 < count($past_events) ) {
      $site_url = get_site_url();
      foreach ( $past_events as $past_event_slug ) {
         $output .= '<li><a href="' . $site_url . '/eventi/' . $past_event_slug . '">' . $past_event_slug . '</a></li>' . "\r\n";
      }
   }

   return $output;
}

add_shortcode("archive", "do_my_custom_archive_render");
function do_my_archive_render($atts) {

   $options = shortcode_atts(
      array(
         'year' => 0,
         'rientro' => 'no'
      ),
      $atts
   );

   $past_event_items="";

   if ( !empty( $options['year'] ) ) {
      global $wpdb;

      $query = "SELECT event_name FROM wp_em_events WHERE EXTRACT(YEAR FROM event_end_date) = %d AND event_end_date < CURDATE()";

      $query = $wpdb->prepare( $query, (int)$options['year'] );

      $past_events = $wpdb->get_col($query);

      $past_event_items = do_my_get_past_events( $past_events );
   }

   $rientro = ( 'si' == "{$options['rientro']}" )? 'yes' : 'no';

   # Uncomment the following 3 lines if you want.
   # if ( empty($past_event_items) ) {
   #    $past_event_items="<li>No Events Found</li>";
   # }

   $custom_short_code="[one_third last="" . $rientro . '" class="" id=""][accordian class="" id=""][toggle title="' . $options['year'] . '" open="no"]<ul>' . $past_event_items . '</ul>[/toggle][/accordian][/one_third]';

   return do_shortcode( $custom_short_code );
}

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