Dear Gary,
That’s unfortunately a question you would have to ask Amex, as the issuer would be the one to determine whether or not you get an additional 30 days.
Also please verify with your credit card company that your Amex insurance will be valid in Panama. Insurance for drivers is required by law in Panama and car rental companies may require you to buy a basic insurance regardless of whether or not you have an Amex, as the car rental company may not (possibly, again please check with them directly) have any way of verifying (that your Amex is enough for your to be compliant with local laws regarding car insurance).
Best regards,
Jessica