Thanks xliioper and USFlyerUS for sleuthing out the fact it could be a Dominican Republic tax.
I'll report back after the AA Refunds Dept. calls me.

If it is indeed a nonrefundable tax, it would have been nice if somewhere in the purchase flow or cost breakdown AA could have mentioned it as being a nonrefundable tax.
I've never purchased a ticket to the DR, so I'd have no way of knowing about it unless I was specifically told.
Don't think it's reasonable to expect travelers to know about a nonrefundable tax on a "fully refundable" ticket, especially if it's not in the fare rules or cost breakdown.

Here's the cost breakdown form the AA website. I can clearly see a $10 tourism tax. It is not attributed to a country like the other fees/taxes are, and most importantly there's no indication it would not be refundable if the ticket is canceled.

Fare, taxes and fees

Adult (per passenger) $1,090.00 USD
PASSENGER FACILITY CHARGE (UNITED STATES) $12.00 USD
TRANSPORTATION TAX (UNITED STATES) $39.40 USD
US APHIS USER FEE (UNITED STATES) $3.96 USD
US CUSTOMS USER FEE (UNITED STATES) $6.11 USD
US FEDERAL INSPECTION FEE (UNITED STATES) $7.00 USD
US SECURITY FEE (UNITED STATES) $11.20 USD
TOURISM TAX $10.00 USD
AIRPORT AUTHORITY FEE (DOMINICAN REPUBLIC) $30.00 USD
AIRPORT DEPARTURE TAX (DOMINICAN REPUBLIC) $20.00 USD
AIRPORT INFRASTRUCTURE FEE (DOMINICAN REPUBLIC) $32.60 USD
Total $1,262.27 USD per person