Andrew Riches, the Davies' lawyer, said the decision was "upsetting" and the Davies were "devastated".
"I thought we'd got there," he said of the appeal.
"Sending her back to South Africa is just not an option for them, it's just too dangerous."
He said the Davies were now considering a further appeal, or hoping Immigration NZ would alter its decision based on a change in circumstances.
"Caitlyn had started making some good progress in New Zealand, and from what I understand, the South African system sees disabled people as a burden on society and wants to move them out of the way.
"For example, in some of the schools in South Africa there are no provisions for blind people in the event of a fire."
Riches said the decision had placed the immigration system at a level of higher importance than the personal circumstances of Caitlyn.
In 2015 Caitlyn's father, Jonathan Davies, arrived in New Zealand from South Africa and was granted a one-year work visa. A few months later Caitlyn, her mother Charmaine and nearly 2-year-old brother arrived, court documents show.
The family moved to the small Canterbury town of Geraldine, where Jonathan has been working as a farm manager.
The family were granted concurrent work and visitor visas, as the partner and dependent children of a worker.
In May 2016, Jonathan was granted a further one-year work visa, while his wife and son were granted concurrent work and visitor visas.
But Immigration NZ declined to grant Caitlyn a visitor visa because she was "not considered to be of an acceptable standard of health".
"Caitlyn's global development delay, blindness and chronic medical conditions were deemed likely to impose significant costs and/or demands on the New Zealand health system," a medical assessor told Immigration NZ.
Her interim visa expired on July 11 last year and she became an unlawful visitor.
On October 25 last year the Immigration and Protection Tribunal of New Zealand issued a decision declining the Davies' appeal against deportation.
Caitlyn was granted a visitor visa for three months effective from October 25 to "enable her parents to plan for and better finance the family's return to South Africa", court documents read.
In March, the Davies family were then granted leave by Justice Cameron Mander to appeal to the High Court in Christchurch against the tribunal's decision to decline the Davies' appeal.
The family argued the tribunal had "erred in law".
Caitlyn's parents believed their daughter should remain in New Zealand because of the poor employment opportunities and limited educational and medical facilities for children with disabilities in South Africa.
They also noted the high incidence of violent crime, including in schools in the African nation.
The tribunal agreed that "given the serious deficiencies" in South Africa Caitlyn's "life chances generally would be far better if she were able to remain in New Zealand".
However, the tribunal argued the desire for families to stay in New Zealand and take advantage of a higher standard of living was common, and disparities in economic opportunities "do not amount to exceptional humanitarian circumstances".
The tribunal said the family were "not destitute before coming to New Zealand" and had not proven they would become so if they returned to South Africa.
It also considered the separation of the Davies family, with the possibility Jonathan might remain in New Zealand to earn a higher wage for his family.
"However, that was tempered by the fact that, initially, the father had come to New Zealand on his own," the tribunal argued.
While Caitlyn did not meet "exceptional humanitarian circumstances" she did, due to her disabilities, face "huge challenges".
The tribunal concluded it maintained its position to deport Caitlyn "to maintain the integrity of the New Zealand immigration system".
In his decision, Nation said he did not consider there to be an error of law from the tribunal.
"It had to weigh the hardship the appellant would suffer against the reasons why she
was liable for deportation.
"The tribunal was not in error in considering the degree of harshness she would suffer against what was 'acceptable to maintain the integrity of New Zealand immigration system'."
He also ruled the tribunal made no error when determining Caitlyn's medical needs would impose a "burden" on public health and special education services.
