Maintenance Template File ignored on Frontpage

I've a problem with Maintenance-Mode ond Druapl 7.59 but only on the Frontpage.

There is a page--front.tpl.php I use in my template folder. In Maintenance-Mode every Site but the Frontpage uses correct maintenance-page.tpl.php from Core (Bootstrap-Sub-Theme in use). I can check this with THEME DEBUG. On the Frontpage I can see in THEME DEBUG that there are several Template-File-Names I can use. There is a page--front.tpl.php and also the maintenance-page-tpl.php.

THEME DEBUG shows then on the Frontpage that page--front.tpl.php is in use. How can that happen in Maintenance-Mode?

I tried to force the use of maintenance-page-tpl.php with 'preprocess_maintenance_page' but not succesfully. Here ist the code:

function MYTHEME_preprocess_maintenance_page(&$vars) {   
    $vars['theme_hook_suggestions'][] = 'maintenance_page';  
}

Thank youu for any help on this.