OP - Your question is odd. It sounds as though your credit line was frozen when your payment was not made due to insufficient funds, but your account was not closed and Amex told you that your account was not closed.

If you have auto pay set up and there are not sufficient funds in the account to cover the payment, you should expect to have your credit line frozen until payment is made. If it happens more than a few times, you should expect to have the account closed.

Don't use auto pay unless you keep sufficient cash on hand to cover payments.