Since she lost the ability to move they have spent 20 hours of every day at her bedside but say they want their daughter to live at home and take advantage of technological developments to extend her ability to interact with the world.
De Moraes Lobo said: "All these doctors signed off that the best course of action was to switch off Ana-Carolina's ventilator and let her die."
It has created a stand-off that the Weekend Herald calculates has tied up one of Starship's 16 intensive care beds for at least three years.
Over that time, Ana-Carolina's care in hospital has cost taxpayers around $4.8 million against $900,000 for care at home.
The strained relationship has seen Health Minister Jonathan Coleman become involved.
The prospect of a withdrawal of care to allow a child to die is a vexed issue well-recognised in medical studies with parents and doctors so opposed they have wound up in the courts.
In Ana-Carolina's case, she is not unwell beyond the condition that has left her paralysed and the health board has told the parents in writing that "withdrawal of active care would never be a unilateral decision by the medical team alone".
But Bircham said the option of "allowing natural death" was the only one put before the parents and it raised the question as to whether other parents in similar situations were deprived of options which should have been available.
"My guess is most people in that situation are encouraged - as we are - to allow their children to die. We were put under considerable pressure for a long period of time."
Bircham said the "natural death" meeting was a "significant turning point" in a relationship which has since suffered almost total breakdown, exacerbated by the lack of a proper system which allowed Ana-Carolina to go home.
Health board documents in the months after "natural death" was rejected make repeated reference to there being no system for gett1ing Ana-Carolina home and raise the cost of doing.
"Setting up such an undertaking will take considerable time and large amounts of planning and money," one stated.
The breakdown in the relationship has seen Ana-Carolina's parents refuse to take steps the hospital says would help their daughter get home - such as training around her ventilator - because of arguments over the level of care she would receive out of hospital.
There have also been accusations over their behaviour, but the couple firmly reject these.
The health board's chief medical officer Dr Margaret Wilsher said there had been efforts since 2014 to get Ana-Carolina home and that was still the plan.
She said Starship had a system for managing children needing breathing support to live at home. It currently had 180 children including nine who needed it for life support.
Dr Wilsher said it was rare to have adult or child patients who were almost completely and reliant on a ventilator to live. She said Starship's view was that children with a ventilator dependency were "far better supported in their own home wherever possible".
The latest effort to discharge Ana-Carolina included a literature review of programmes in other countries to benchmark care in New Zealand. There has also been a review of the case by an Australian expert and the appointment of an independent panel of experts to review plans to move Ana-Carolina from the paediactric intensive care unit.
Ministry of Health chief advisor on child health Dr Pat Tuohy said New Zealand had not adopted a 2008 consensus statement around the care of children seeking home ventilation because it was a "rare situation". Instead, such children were managed on a case-by-case basis, he said.
The Weekend Herald asked Minister of Health Jonathan Coleman questions about why the 2008 consensus statement on home ventilation hadn't been introduced, how the health budget was matched against the increasing ability to maintain or prolong life and what systems existed around end-of-life decision-making.
He said the questions all related to an "especially tragic and difficult" case and he would not comment as a result.
How to help
givealittle.co.nz/cause/anacarolina
