The Cantrell family from Illinois were looking forward to their annual trip to the beach resort of North Carolina.
Last fall, their plans had changed after the death of their 9 year old daughter who had suffered a asthma attack.
The mother of the family said that even though they had their travel booked, including their airline tickets, the family had decided to change their plans after eldest daughter of the family had decided that it would be too painful for them to go on their vacation without her beloved sister.
The eldest daughter, named as Katie had told NBC5 that it was too emotional for them all to go back there this year without her and "would never be as much fun without her."
The family then tried to cancel their American Airlines tickets, but the carrier refused to offer a refund for the ticket of the deceased girl.
American Airlines Group said "the ticket purchased is non-refundable so we cannot offer a refund, issue a ticket voucher, or transfer this ticket to another person."
On Tuesday evening, American Airlines had got in touch with the family, apologised for how the situation was handled and have now refunded the ticket as well as an apology and their condolences.