Confirming loading mostly untill PHP max_execution time is reached.
From PHP-FPM (5.4.x) slowlog:
[0x00007f23a2d13838] file_get_contents() /var/www/clients/client1/web1/web/wp-content/plugins/wp-maintenance-mode/inc/key-check.php:47
[0x00007f23a2d136b0] lrss_check_update() /var/www/clients/client1/web1/web/wp-content/plugins/wp-maintenance-mode/inc/key-check.php:52
[0x00007fff91fa7050] lrss_updatefunction() unknown:0
[0x00007f23a2d12eb8] call_user_func_array() /var/www/clients/client1/web1/web/wp-includes/plugin.php:487
[0x00007f23a2d12c00] do_action_ref_array() /var/www/clients/client1/web1/web/wp-includes/query.php:2872
[0x00007f23a2d12af8] have_posts() /var/www/clients/client1/web1/web/wp-includes/query.php:743
After disabling this Plugin site runs perfect again. Note: Maintenance site is loading fine if “Maintenance mode” is actually enabled.
Other than stated by emielm it’s not resolved by disableing the “Support” option.