maintenance page whit sub-subtheme

What you've done is probably correct, but you need one more change in your settings.php file.

The maintenance theme needs to be set from $conf in the settings.php file (so users don't accidentally mess up the maintenance theme and lock themselves out of the site).

In settings.php, change lines 172-213 so it looks something like this:

$conf = array(
# 'site_name' => 'My Drupal site',
# 'theme_default' => 'minnelli',
# 'anonymous' => 'Visitor',
/**
 * A custom theme can be set for the off-line page. This applies when the site
 * is explicitly set to off-line mode through the administration page or when
 * the database is inactive due to an error. It can be set through the
 * 'maintenance_theme' key. The template file should also be copied into the
 * theme. It is located inside 'modules/system/maintenance-page.tpl.php'.
 * Note: This setting does not apply to installation and update pages.
 */
   'maintenance_theme' => 'your_theme',
/**
 * reverse_proxy accepts a boolean value.
 *
 * Enable this setting to determine the correct IP address of the remote
 * client by examining information stored in the X-Forwarded-For headers.
 * X-Forwarded-For headers are a standard mechanism for identifying client
 * systems connecting through a reverse proxy server, such as Squid or
 * Pound. Reverse proxy servers are often used to enhance the performance
 * of heavily visited sites and may also provide other site caching,
 * security or encryption benefits. If this Drupal installation operates
 * behind a reverse proxy, this setting should be enabled so that correct
 * IP address information is captured in Drupal's session management,
 * logging, statistics and access management systems; if you are unsure
 * about this setting, do not have a reverse proxy, or Drupal operates in
 * a shared hosting environment, this setting should be set to disabled.
 */
# 'reverse_proxy' => TRUE,
/**
 * reverse_proxy accepts an array of IP addresses.
 *
 * Each element of this array is the IP address of any of your reverse
 * proxies. Filling this array Drupal will trust the information stored
 * in the X-Forwarded-For headers only if Remote IP address is one of
 * these, that is the request reaches the web server from one of your
 * reverse proxies. Otherwise, the client could directly connect to
 * your web server spoofing the X-Forwarded-For headers.
 */
# 'reverse_proxy_addresses' => array('a.b.c.d', ...),
);

In other words, uncomment lines 172, 184, and 213, and then change line 184 to point to your theme's name.