From AMEX
"U.S.Consumer Basic and Additional Platinum Card® Members may receive up to a total of $200 in statement credits each calendar year, across all Cards on the Account, when using their eligible Platinum Card on eligible, prepaid Fine Hotels + Resorts® and The Hotel Collection bookings made through American Express Travel (meaning through amextravel.com, the Amex® App, or by calling the phone number on the back of your eligible Platinum Card)."

Sounds like it can include more than one transaction.