CEO Ben Baldanza also issued a statement saying the airline's refund policy is part of the reason the discount airline can keeps fares low, but failing to refund dying veteran Jerry Meekins his fare was a "mistake."
The statement also said Baldanza would "personally" refund the veteran's money and the airline would donate $5,000 to "the charity of his choice, Wounded Warriors."
The controversy began when a doctor told Meekins he should not fly. Spirit Airlines then refused to refund his ticket price of $197, Fox News reported Saturday.
That sparked a flurry of criticism from veterans and a Facebook campaign calling for a boycott of the airline.
Within a week the "Boycott Spirit Airlines" Facebook page had 30,000 supporters and a second Facebook page was calling for the airline's board to fire its CEO.
Baldanza then issued an apologetic statement that said, "A very important part of keeping our airfares reasonably priced is our refund policy.
"Every day we seek to balance customer service with customers' demands for the lowest airfare possible. But sometimes we make mistakes," the statement said.
"He called me personally, and I'm going to take him at his word," Meekins said.
Meekins also said he would never fly Spirit Airlines again.
"In my opinion, and this is just a guess, but the board of directors might have called him up and said, 'Baldanza, what the hell are you doing?'" Meekins speculated. "Give the man back his money."