Sorting past events by month

Using query_posts is pretty much always a bad idea as it causes another database query but it also will break pagination and can cause other issues as well.

What you need it a filter on pre_get_posts.

function pgp($qry) {
  if (!is_admin() && is_main_query() && $qry->is_category(3709)) {
    $qry->set('orderby','meta_value');
    $qry->set('meta_key','Deadline'); //formatted YYYYMMDD
    $qry->set('ignore_sticky_posts',true);
  }
  return $qry;
}
add_filter('pre_get_posts','pgp');

That is assuming that category ID 3709 is the “past-event” category. Once you’ve done that follow the answer by @KrzysiekDrozdz