AJAX: Form API Dependent Drop Down with more options
Not totally sure, but setting $form_state['rebuild'] = TRUE in your submit or validation handler may help here.


  This is the key function for making multi-step forms advance from step
  to step. It is called by drupal_process_form() when all user input
  processing, including calling validation and submission handlers, for
  the request is finished. If a validate or submit handler set
  $form_state['rebuild'] to TRUE, and if other conditions don't preempt
  a rebuild from happening, then this function is called to generate a
  new $form, the next step in the form workflow, to be returned for
  rendering.


https://api.drupal.org/api/drupal/includes!form.inc/function/drupal_rebuild_form/7

Another option would be to replace the entire form on in your AJAX callback. So essentially you'll specify a #prefix and #suffix for the entire form and then use that prefix element id in your $form['dropdown_first/second']['#ajax']['wrapper']. Your callback will look something like this:


function ajax_example_dependent_dropdown_callback($form, $form_state) {
  ...
  return $form;
}