Sometimes banks may block certain charges from going through as a way to prevent fraud. This may be due to them not seeing your purchase as a regular spending pattern or simply because the dollar amount being put through the card is not something they would see normally on your end.
Often times a quick call to the issuing bank of your credit card and letting them know that you, the cardholder, is authorizing the charge will solve the issue and unblock your card for use 99% of the time.
Yes, we do accept American Express Payments using PayPal; a PayPal account is not required to pay using your American Express card