I don't know the reason, but it looks like jQuery UI's accordion hasn't been able in "cloning" event-handlers to the new elements.
There's a method called .refresh() in accordion, which (according to its doc.) should solve this, but sadly it doesn't. So I played a a little longer with your fiddle, and added 2 lines to this event-handler of yours:
$(AddButton).click() //on add input button click
- to the very start, just destroy accordion first ...with this:
- then right before returning false, add this: