If you are using Magento's Maintenance mode whilst you're trying to configure, setup and test Shiptheory, you will need to make sure you allow Shiptheory's servers through maintenance mode.  The easiest way to do this is to allow the API to be used whilst keeping the maintenance (503) pages displayed.

Taken from here you can modify your index.php file as seen below:

In root index.php file

if (file_exists($maintenanceFile) && !strstr($_SERVER['REQUEST_URI'], 'api/?wsdl')) {
    include_once dirname(__FILE__) . '/errors/503.php';

Remember to backup any changes you're making incase of complications.  Each Magento configuration and server setup can be different.  Whilst this solution should work for 99% of cases you may have mod rewrites or other systems/solutions that conflict with this one.