Problems wp_insert_post and save_posts filter

you can check what post type is calling the ‘save_post’ action
try:

public function save() {
global $post;
  if (!$post->post_type="video"){
    $my_child = array(
                'post_title' => $this->_child_type,
                'post_content' => "test content",
                'post_status' => 'publish',
                'post_type' => "video",
                'post_parent'=> 55
              );
    $nindex = wp_insert_post($my_child);
  }
}
add_action('save_post', array(&$this, 'save'));