Ajax form hidden default value not returning values when ajax runs

I have a custom where I need to render a calendar, but only shows the whole week of the current week.

I've added an element for the date where I've set the default value to something like below (actual code):-

$form['container']['date'] = array(
  '#type' => 'hidden',
  '#default_value' => $default_date,
);

My button is ajax and the type is just a button. These buttons are like previous month, next month, previous week and next week. Like below (actual code):-

function booking_calendar_form($form, &$form_state) {
  $selected_date = 'today';
  if (isset($form_state['values']['date']) && !empty($form_state['values']['date'])) {
    $selected_date = strtotime($form_state['values']['date']);
    if (isset($form_state['triggering_element']['#name'])) {
      if ($form_state['triggering_element']['#name'] == 'previous_month') {
        $selected_date = strtotime('-1 month', $selected_date);
      }
      elseif ($form_state['triggering_element']['#name'] == 'next_month') {
        $selected_date = strtotime('+1 month', $selected_date);
      }
      elseif ($form_state['triggering_element']['#name'] == 'previous_week') {
        $selected_date = strtotime('-1 week', $selected_date);
      }
      elseif ($form_state['triggering_element']['#name'] == 'next_week') {
        $selected_date = strtotime('+1 week', $selected_date);
      }
    }
    $selected_date = format_date($selected_date, 'custom', 'Y-m-d');
  }
  elseif (isset($params['date']) && !empty($params['date'])) {
    $selected_date = $params['date'];
  }
  $selected_date = $default_date;
}

When the ajax runs, the hidden type value emptied. Not sure what's wrong with my code. Here is how I render the buttons (actual code):-

$form['navigation']['prev_month'] = array(
  '#type' => 'button',
  '#value' => t('Previous month'),
  '#name' => 'previous_month',
  '#ajax' => array(
    'submitter' => FALSE,
    'callback' => 'calendar_ajax_callback',
    'event' => 'mousedown',
    'wrapper' => 'container-wrapper',
    'method' => 'replace',
    'effect' => 'fade',
  ),
);

Form output/container:-

$form['container'] = array(
  '#type' => 'container',
  '#prefix' => '<div id="container-wrapper">',
  '#suffix' => '</div>',
);
$form['container']['date'] = array(
  '#type' => 'hidden',
  '#default_value' => $default_date,
);
$form['container']['header'] = array(
  '#markup' => $header_navigation,
);
$form['container']['calendar_display'] = array(
  '#type' => 'markup',
  '#markup' => $output,
);

Returning ajax callback:-

function calendar_ajax_callback(&$form, &$form_state) {
  $form = booking_calendar_form($form, $form_state);
  return $form['container'];
}

What's wrong with my code? Please help.