Adam Levitt says he's booked numerous flights for the Business Select class, which gave travelers drink coupons worth $5 each.
The coupons have no expiration date, but Southwest recently changed its policy so that they have to be used on the day of travel.
Levitt claims that's a breach of contract and filed a federal lawsuit against the carrier.
Southwest says it's reviewing the claim.
The lawsuit seeks class-action status for Southwest customers nationwide who have unredeemed drink coupons.
The Associated Press contributed to this report.