Thank you for reaching out about this! Generally when a domain authorization fails the money spent will be automatically returned to your account. This can take some time though depending on your banking institute.
I would recommend reaching out to our live support team so they can review the purchase and help you with getting this domain connected to your account. To contact our live support please follow this link: Shopify Help Center - Contact Support, sign into your store account, search for "domain purchase issues" and use the contact support button at the bottom of the search results to see all our live support options.
Shay | Social Care @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog