Ted here from Shopify, thanks for reaching out to us!
This is a great question. At the moment there doesn't seem to be any issues when buying a domain so it does look like it could be a payment issue. Are you trying to purchase the domain using a credit/debit card or via Paypal? Could you describe what happens when you try to buy the domain? For example, does a warning banner appear on the screen after? I'm happy to take a closer look into this with you but first I would need to authenticate your account via email.
If you are trying to pay for the domain using Paypal but the payment is failing, then you will need to contact Paypal's customer service here for more info. You can choose to pay for the domain using a credit card instead too if you would prefer. You can add this to your account by selecting Settings > Billing > Add payment method in your admin as shown here.
If both of the options above do not suit, don't forget that you can always buy the domain from another domain registrar and then you can point it to Shopify as shown in this guide.
If there is anything else I can help you with, please let me know, I'm happy to help!