American Airlines came under fire this week after a customer service problem was posted on Facebook and went viral.

An Illinois family booked roundtrip flights to North Carolina for a vacation, but cancelled the trip after one of their daughters passed away. The family was shocked to learn that their late daughter's ticket would not be refunded.

The Cantrell family's spring break trip was nixed after Madison, a fourth-grader, passed away from an asthma attack five months ago. Her older sister, Katie, said she could not take the vacation.

"Emotionally, I couldn't go back there this year without her," the 13-year-old told NBC Chicago. "It would never be as much fun without her."

The family submitted documentation to American Airlines proving that Madison had passed away, and received a response four months later.

"After reviewing the documentation submitted, it has been determined the request does not meet our exception requirements," a letter from the airline read. "The ticket purchased is non-refundable so we cannot offer a refund, issue a travel voucher, or transfer this ticket to another person."

According to the company's website, however, "in the case of the death of the passenger/immediate family member/or a traveling companion the change fee may be waived or the ticket refunded provided a copy of the death certificate is presented to American Airlines."

Madison's mother, Felicity, said she was stunned by the terse and contradictory response.

"Clearly, this has struck a chord with people," she said of the hundreds of Facebook comments her story received. "We can't be the only family this has happened to."

Felicity and Katie insisted that their conflict with the airline was "not about the money."

"I know that I would never write this to someone," Katie said. "I don't know how someone could send this to another family. I would never want to be treated that way and I would hope no one would ever treat anyone else that way."

American Airlines issued a public apology on Tuesday.

"We extend our deepest sympathies to the Cantrell family on the loss of their daughter, Madison," a spokesperson told NBC 5 Investigates. "We fully refunded Madison's ticket last night and apologised to Mrs Cantrell for not doing so immediately when she first contacted us."