Showing taxonomy child terms on archive page

I’m using the code below for showing the current parents child terms in a sidebar, which generates a nice menu for navigating. However, once I visit the child term archive page, the menu doesn’t show anymore, since the code only looks for direct child terms of a parent.

If anybody has a solution for this, I really appreciate it.

<?php
                $term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
                $taxonomy     = 'categorie';
                $show_count   = 0;
                $pad_counts   = 0;
                $hierarchical = 1;
                $title        = '';

                $args = array(
                'taxonomy'     => $taxonomy,
                'orderby'      => $orderby,
                'show_count'   => $show_count,
                'pad_counts'   => $pad_counts,
                'hierarchical' => $hierarchical,
                'title_li'     => $title,
                'child_of'     => $term->term_id
                );
                ?>