wp_get_archives() not working for my custom post type

I have my custom post type working, but I can't seem to get the archives working.

Here is my code for getting the archives:

  ul
   ?php 

   $args = array(
    'type'            = 'monthly',
    'limit'           = '',
    'format'          = 'html', 
    'before'          = '',
    'after'           = '',
    'show_post_count' = false,
    'echo'            = 1,
    'order'           = 'DESC',
    'post_type'     = 'my_custom_post_type'
  );

  wp_get_archives( $args ); ?
  /ul

Here are the args for my CPT:

$args = array(
    'label'                 = __( 'My Custom Post Type', 'realtextdomain' ),
    'description'           = __( 'What We Are Reading Custom Post', 'realtextdomain' ),
    'labels'                = $labels,
    'supports'              = array( 'title', 'editor', 'excerpt', 'author', 'thumbnail', 'comments', 'revisions', 'custom-fields'),
    'hierarchical'          = false,
    'public'                = false,
    'show_ui'               = true,
    'show_in_menu'          = true,
    'menu_position'         = 5,
    'show_in_admin_bar'     = true,
    'show_in_nav_menus'     = true,
    'can_export'            = true,
    'has_archive'           = true,
    'exclude_from_search'   = true,
    'publicly_queryable'    = false,
    'menu_icon'             = 'dashicons-book',
    'capability_type'       = 'post',
    'rewrite' = array('slug' = 'my_custom_post_type_slug'),
);

register_post_type( 'my_custom_post_type', $args );

I have flushed permalinks, but still nothing showing up for me... any ideas on what I'm doing wrong?