wpquestions.com, ID = 3784

<?php

/**
 * auto add child terms to nav menus
 */
function custom_walker_nav_menu_start_el ( $item_output, $item, $depth, $args) {

    // filter only taxonomy menu items
    if( $item->type == 'taxonomy' ) {

        // set args
        $args = array(
            'taxonomy' => $item->object,
            'child_of' => $item->object_id,
            'echo' => 0,
            // 'hide_empty' => 0,
            'show_option_none' => '',
            'title_li' => ''
            );

        // check for children
        $children = wp_list_categories( $args );

        // if any, append them as a list
        if ( $children )
            $item_output = $item_output . '<ul class="children" >' . $children . '</ul>';

    }

    return $item_output;

}

add_filter( 'walker_nav_menu_start_el', 'custom_walker_nav_menu_start_el', 10, 4 );