I have been trying to figure out how to renew my domain for the longest time. I had it set on auto-renewal but the payment failed due to me changing my card number and not updating my payment. How can I get my site domain running and active again? There aren’t any options for me to renew with my new payment I have added 
Here’s the answer from Shopify help docs
If you don’t have auto-renewal enabled for your domain, then you need to manually renew your domain to prevent it from expiring.> > If your domain subscription expires, then you have 40 days tocontact Shopify support if you want to renew it. You can’t renew an expired domain yourself.
Consider sending a quick email to Shopify’s Merchant support. They should assist you with the issue!
Contact page link: https://help.shopify.com/en/questions#/contact/email