If you have done every process online, then it will take from three days to seven days to get the refunds. If you had used debit or credit cards, then it is going to take at least fifteen days. To get a full refund. However, it is going to be more delayed in case you had paid via check. Then it will easily take around 30 days to process. You cannot do anything about it since it is the rules implemented by the American Airlines Refund policy. One more thing, if you are asking for a refund still with the paper voucher, then you need to mail the original coupons to American Airlines' official address situated in Phoenix.