Add javascript to views exposed form after ajax submit
You'll need to wrap the JS in a Drupal behaviour, so that it is attached after the ajax refresh.

You should also ensure it only runs once

 Drupal.behaviors.styledSelect = {
   attach: function() {
     $('select').once('ss', function() {
       $(this).styledSelect();
     }
   }
 };


That way it won't get 'styled' on every ajax change.