Why post__not_in is ignored?

As per the Codex entry:

“post__not_in (array) – use post ids. Specify post NOT to retrieve. If this is used in the same query as post__in, it will be ignored.

Try to make an array of the post id’s you do want to display, OR an array of the post id’s you want to exclude instead of trying to do both.

Edit: If you want to exclude a particular set of pages, with your current code, you would simply remove the conflicting ‘post__in’ parameter you have in your $args, and your query should work after:

$exclude_ids = array(294,278,6758,9582,9674,8638,8585,7359);
$args = array(
        'paged'          => $paged,
        /***** 'post__in'       => $ids, ***** Remove this line *****/
        'post__not_in'   => $exclude_ids,
        'posts_per_page' => -1,
        'post_type'      => 'page',
        'orderby'        => 'menu_order',
        'order'          => 'ASC'
);

$my_query = new WP_Query($args);