I've had headaches in the past trying to render a Drupal menu with not only the parent links, but also all of their children. I've used modules like Nice Menus in the past but it's kind of a messy solution if you just need to print sub-menus.

I did come up with a solution, and I thought I'd post it. Hope it's useful to you!

In your template.php

function ThemeName_process_page(&$vars) {
$menu_tree = menu_tree_all_data('your-menu-name');
$vars['menu_expanded'] = menu_tree_output($menu_tree);
}

Tags: 

drupal 7 theming
menu system
sub menus
Planet Drupal