Just an FYI to anyone else who may come across this thread, here is the response I received from Customer Support:

"If you're receiving an error code 401 while attempting billing, the transaction has been declined. We apologize for any inconvenience this may have caused. Reasons for the error may include but are not limited to:

- The transaction being declined by the bank
- Incorrect information provided for the card
- Use of pre-paid debit or credit cards
- Card information not matching Account information
- Cards being used on multiple SQUARE ENIX Accounts
- Insufficient funds available on the card
- Attempting different cards in rapid succession

While the transaction may have been declined automatically for any of these reasons, there are additional reasons that may have caused the error.

Please do not attempt to continue using a declined card as it may cause a temporary lockout from billing on the account. If you're receiving a billing declined error, it is possible there is a temporary lockout on the account. When receiving 401 errors, please wait a minimum of 24 hours from the most recent attempt before reattempting the transaction."

I bolded the most important statements in my opinion. Because typically when a card receives an error, people with multiple cards will try another, which is what I did. Little did I know, that once a transaction receives an error, you have to wait a minimum of 24 hours before reattempting. I waited over 36 hours and just tried the card that I had previously successfully purchased with, and it worked just fine. I just wish they would post this information along with the error message, it would help a lot.

It is also worth noting that your SE account address MUST MATCH your bank mailing address EXACTLY. I know when I first setup my account, my bank had my address listed with the apartment on the second line of the address, but SE doesn't allow for multiple line addresses, so I had to change the address with my bank so that the street address and apartment were on the same line.