new WP_query > displays posts only once instead of running through full array

You can iterate over the array of IDs and look for the corresponding post in your results to generate output with duplicate posts:

$post_ids = array( 208, 212, 218, 208, 212, 218 );

$args = array(
    'post_type' => 'custom_posttyp',
    'order_by' => 'post__in',
    'post__in' => $post_ids,
);

$the_posts = get_posts( $args );

foreach( $post_ids as $id ){
    foreach( $the_posts as $a_post ){
        if( $id == $a_post->ID ){
            echo get_the_title( $a_post );
        }
    }
}