I'm a little confused. When you refresh the page, what do you see? The original order, or the newly sorted order?
If the latter, then there's no need to refresh the page at all. That's the whole point of an Ajax sortable -- your page layout is persisted back to the database, so you don't have to refresh the page. The new order is the new DOM order and (after a little back-channel traffic, is the new database order, too.
If you're looking for some confirmation that the new order "took", you might want to look at the highlight callback.