Rutgers started making the visa application almost immediately after finding out about his nephew's death, and flew to the High Commission on Monday.
The funeral was planned for Saturday May 25, and the couple had planned to fly out of Auckland today. (Tuesday 21).
Instead, they are still in Wellington, after having been told by the High Commission that the emergency visa criteria no longer existed and normal processing time applied.
Owens, a New Zealand citizen, was told it would take over a week to have her visa processed and the funeral would have been over by then.
Rutgers said his nephew, the son of his eldest sister, was "like a son" to him and had lived with him as a child.
"Loved ones don't give a notice before they die unfortunately, and having to wait 10 days or more for a visa is just not good enough," Rutgers said.
Fine Travel agent Donna Baker, who specialises in African travel, said Rutgers was one of two clients she had this week who were struggling to get visas to fly home for funerals.
Baker said she knew of dozens of others who had encountered similar situations because of the South African visa policy.
She has started an online petition calling for emergency visas for South Africans on New Zealand passports to be reinstated.
"In what I do, I deal with a lot of bereavement and emergency travel unfortunately," Baker said.
"It can be really painful seeing families after families missing funerals and unable to say goodbye to their loved ones."
A Ministry of Foreign Affairs and Trade (Mfat) spokeswoman said she understood the South African High Commission was no longer issuing emergency visas.
"Mfat has highlighted to the South African High Commission the difficulties this is causing some New Zealanders," she said.
"The ministry understands the distress that families can face in difficult times.
"While Mfat is unable to interfere in the immigration and visa policies of another country, we continue to regularly engage with the High Commission to highlight difficulties faced by New Zealanders in getting visas."
However, she said, it welcomed a recent announcement from the South African Government that it intended to use NZ as the pilot for a new electronic visa scheme.
The programme will allow returning South Africans and travellers to apply for visas to be processed electronically, thus cutting out interactions with immigration officers.
"Once implemented, it is hoped this will improve the experience for New Zealanders applying for visas to travel to South Africa."
A South African High Commission spokesman said while it appreciated the concerns raised in regard to its visa process, it would like to remind all that its "visa regulations are not subject to NZ laws".
The spokesman said visa applications had a turnaround time of seven to 10 working days, which was in line with the provisions under the Immigrations Act of South Africa.
"The High Commission unfortunately is not in a position to change the law, it is only an implementing arm of the regulations," he said.
"The figures relating to visa issues is strongly related to the security of South Africa, and can unfortunately not share that information with any institutions outside of the South African Government."
