The parents of a 10-year-old girl in the U.S. have made public details of the appalling service they got when United Airlines "lost" their daughter midway through her trip from San Francisco to Traverse City, Mich., for summer camp.

Annie and Perry Klebahn of San Francisco have made public a complaint letter to the airline detailing how the company lost track of their daughter, Phoebe, on a June 30 flight during a transfer at Chicago’s O’Hare airport. The journey would become a harrowing one for the family involving a byzantine set of phone calls to locate their missing child as well as her luggage.

Phoebe was expressedly told "only go with someone with a United badge on and that she would be accompanied at all times," according to the couple.

The Klebahns were worried when the camp in Michigan called to say their daughter had not arrived.

According to the letter, Annie Klebahn called a customer line which connected her with United’s service centre in India. After a 20-minute wait, the person on the line told the Klebahns that their daughter had arrived in Traverse City. When Annie Klebahn got upset, she was put on hold again – for 10 minutes – and was then told Phoebe was indeed in Chicago and had missed her connection.

Meanwhile, Perry Klebahn, who is a United Premier member, had called a different line – getting hold of a customer service representative in the U.S.

She told him the "unaccompanied minor service" in Chicago "forgot to show up" to transfer Phoebe to the next flight.

The Klebahns said in their complaint letter they had never been told "that United outsourced the unaccompanied minor services to a third party vendor. "

When he begged the person to locate his daughter, she said she was going off shift and could not help. He pleaded with her, asking if she was a mother. When she said yes, he asked what would she do if she couldn’t locate her child for 45 minutes. In 15 minutes, the employee found Phoebe.

Asked 3 times to use the phone

In speaking with their daughter, the Klebahns discovered:

When Phoebe landed, no one was there to get her.

The attendants told their daughter they could not help her and to wait.

She asked three times to use a phone and they told her to wait.

Phoebe then missed her flight and informed a United employee and asked them to make sure the camp in Michigan knew she was late. She was told United would "take care of it."

Phoebe managed to arrive four hours later – sans luggage. That marked yet another saga for the Klebahns, who say they sent camp officials to the airport in Michigan five times before the luggage arrived.

The Klebahns asked for a refund of the $99 charge for the unaccompanied minor service – they had paid the camp $25 every time to go to the airport for the luggage.

The couple filed a formal complaint with the airline in mid-July and addressed a letter to the airline’s CEO. At the time, the couple could not get a response concerning their complaint.

The Klebahns called it their worst customer service experience, ever – spending an estimated 18 hours on the phone.

When local news in San Francisco took an interest in the Klebahn’s story in August, the airline responded. And on Aug. 13, company officials released a statement saying they had apologized to the family and are "reviewing the matter."

"What the Klebahns describe is not the service we aim to deliver to our customers. We are redepositing the miles used to purchase the ticket back into Mr. Klebahn’s account in addition to refunding the unaccompanied minor charge"