It was stopped when he was 5 on the grounds that he no longer met the criteria of needing "attention and supervision substantially in excess of that normally required by a child of the same age and gender".
Instead, his mother Noelene Reid was awarded the princely sum of $1.30 a week as a disability allowance for Zach.
The disability allowance is an income-tested payment of up to $61.38 a week to cover the actual medical and other costs of a disability. It can be paid in addition to the child disability allowance, which is a non-income-tested fixed amount of $46.25 a week to recognise the extra care and attention required for a disabled child.
Zach's asthma has got better as he has got older. In his early years he often had to go to hospital, but last year he went only once.
But he still needs two puffs a day on Ventolin, which costs $18 a month, and two adult doses of asthma preventer Serevent, at $5 a month.
In winter, he gets wheezy two or three times a month. He then needs to take steroid medication Redipred, at $10 a month, and a daily tablet, Singulair, costing $96 a month.
"He's supposed to take Singulair every day but I don't give it to him every day because I can't afford it," Ms Reid said.
Doctor's visits cost another $10 a visit about three times a month in winter.
Ms Reid said the steroids Zach takes when he is wheezy makes him "hyper" and she is afraid to send him to school on those days after she found him with blood all over his face when he ran into a wall.
"He takes probably a good 10 weeks off school a year," she said.
For that reason Ms Reid can't get a job and survives on a sole parent benefit. She also receives a $60 a week disability allowance for her own asthma, which covers medical, heating and lawnmowing costs.
Beneficiaries Advocacy and Information Service (BAIS) manager Karen Pattie said Zach's $1.30 disability allowance appeared to be an error based on the $61.38 maximum. She said parents and children were entitled to separate disability allowances of up to $61.38 each.
What is the allowance?
The allowance is unusual because it is not income-tested and pays a child's principal caregiver a flat amount, currently $46.25 a week, to recognise the "extra care and attention" that a disabled child needs.
CCS Disability Action policy manager Sam Murray said the numbers on the allowance increased in the decade to 2009 because of growing recognition of conditions such as autism and dyslexia. The cost leapt from $28 million in 1997-98 to $102 million in 2009-10, and has been cut to $84 million this year.
"So in 2007 they decided to review it," he said. "They only consulted the medical professionals and they made several changes. The re-did the medical certificate, they introduced new guides for both doctors and case managers, and they required consultation with new regional health advisers. They said the level of care required is high."
The new guide for doctors says, for example, that a 7-year-old with dyslexia can get the allowance if she is "unable to toilet, dress herself, play safely without supervision and doesn't recognise obstacles or dangers".
But a 9-year-old dyslexic child who can take care of himself and avoid dangerous situations would not qualify.
Wellington advocate Graham Howell said one family with an intellectually disabled son lost the allowance when the boy grew old enough to tie his own shoelaces. A child with eczema lost the allowance when he became able to apply his own ointment.
"It's a very, very narrow definition of 'extra care and attention'," he said.
Thames parent Jacqueline McGrath, whose son Cullen-lee was born with cerebral palsy and epilepsy, said she and her husband were shocked when another parent mentioned the child disability allowance when Cullen-lee was in intensive care in hospital, aged 3.
"We were just like, 'Disability what?'" she said.
Auckland social worker Nicola Chapman said that despite her professional background she didn't hear about the allowance until two and a half years after her son Daniel was born with a severely disabling neuromuscular condition.
Onehunga mother Emma-Rose Cottrell only found out about it last year when her son Jack was 8. His autism has been apparent since he was 3 or 4, Mrs Cottrell looks after him full-time and her husband works only part-time.
"He's not allowed to do full-time, otherwise I'd die of stress," she said. "I have to do naps most days, I am just exhausted."
When she finally heard about the allowance, it was "an absolute godsend".
"I get about $90 a fortnight," she said. "That $90 is enough to stop us from starvation and poverty."
Social Development Ministry manager Carl Crafar said the numbers of new child disability allowances granted rose again in the past two years. Applications that were declined fell from 20 per cent in 2012 to 15 per cent last year.
On the web:
www.cpag.org.nz
www.bais.org.nz
Rise reversed
Children with child disability allowances
Number % of all children
1998 17,587 1.7%
1999 19,320 1.9%
2000 20,864 2.0%
2001 21,724 2.1%
2002 23,748 2.3%
2003 27,342 2.6%
2004 31,471 2.9%
2005 33,050 3.1%
2006 36,207 3.3%
2007 39,145 3.6%
2008 43,185 4.0%
2009 45,767 4.2%
2010 43,883 4.0%
2011 39,253 3.6%
2012 36,894 3.4%
2013 34,968 3.2%
2014 34,501 3.1%
Source: Ministry of Social Development