Você precisa alterar child_of
para post_parent
e também adicionar post_type => 'page'
:
WordPress codex Wp_query Postar & Parâmetros da Página
<?php
$args = array(
'post_type' => 'page',
'posts_per_page' => -1,
'post_parent' => $post->ID,
'order' => 'ASC',
'orderby' => 'menu_order'
);
$parent = new WP_Query( $args );
if ( $parent->have_posts() ) : ?>
<?php while ( $parent->have_posts() ) : $parent->the_post(); ?>
<div id="parent-<?php the_ID(); ?>" class="parent-page">
<h1><a href="<?php the_permalink(); ?>" title="<?php the_title(); ?>"><?php the_title(); ?></a></h1>
<p><?php the_advanced_excerpt(); ?></p>
</div>
<?php endwhile; ?>
<?php endif; wp_reset_postdata(); ?>