Your hosting provider may have a security measure enabled that must be fixed on the host side in order to connect your store with Printful.
Give HostGator a shout on their live chat line and let them know you're not able to integrate Printful with your store. They'll be able to see a report for your account that tells them what needs to be whitelisted. This seems to be a common error for them and is noted in their FAQ here.
When talking to HostGator, mention the keyphrase "Whitelist rule ID 1234234". This will point them to the right settings to adjust. They'll also need to know Printful's IP addresses - you can email us at email@example.com to ask for the current ones.