This isn't a bug in the module, but an IE11 bug that affects CKEditor and requires a workaround. Bug is posted to CKEditor issue queue here: http://dev.ckeditor.com/ticket/11342#comment:16.

I'm posting a Drupal-based workaround for posterity:

/**
 * Implements hook_element_info_alter().
 */
function examplemodule_element_info_alter(&$types) {
  // For textarea fields, add a pre-render callback to include bug fixes.
  $types['text_format']['#pre_render'][] = 'examplemodule_ckeditor_pre_render_text_format';
}

/**
 * Adds examplemodule.js, which contains JS bug fixes for ALL themes.
 */
function examplemodule_ckeditor_pre_render_text_format($element) {
  drupal_add_js(drupal_get_path('module', 'examplemodule') . '/js/examplemodule.js');

  return $element;
}

examplemodule.js:

(function ($) {

  Drupal.behaviors.exampleModule = {
    attach: function (context, settings) {
      // Bug fix for IE11, which causes problems with CKEditor when jQuery UI
      // tabs are clicked.
      // @see http://dev.ckeditor.com/ticket/11342#comment:16
      $('.vertical-tab-button a', context).click(function() {
        $('.cke_editable > p:contains("<br></br>")').remove();
      });
    }
  };

})(jQuery);