The other day I realized that I had never saved my Google Authenticator secret key.
I do not think your mistake is uncommon. In the future you do not have to reset your authenticator. You disable it and re-enable it. When you re-enable it they provide a different code. This action in itself should not freeze your account.
This is one reason why I don't fall in love with Google Authenticator though I understand that it is really providing a good measure of security which we badly need these days when there are so many scammers and hackers just lurking somewhere ready to victimize us out of our hard-earned money. This has become a necessary burden but am hoping it can still be improved to make it more convenient without sacrificing its security features.