First, need to lose `query_posts()` - it should never be used for secondary loops.

Try something like this:

    $posts = get_posts( array(
        'cat' => $category->term_id,
        'numberposts' => 3,
        ));
    
    foreach( $posts as $post ) {
    	
    	$listing_code .= get_permalink( $post->ID ); //or whatever
    }