Last month, William was placed on life support when suffering pneumonia. He recovered and returned home until the latest infection struck.
"He hasn't really improved that much. He's got very tight breathing. He's being supported with some oxygen. We don't think he's in any danger.
"This is his sixth hospitalisation for respiratory illness and he's not in that much danger."
Recently, Wellington Hospital told the Burtons that William won't go back on life support - a decision Starship Children's Hospital in Auckland backed up in a second opinion.
Both hospitals say they are unable to discuss that decision for privacy reasons but the Burtons say they do not accept it.
"With each illness his lungs get a little bit worse, which leads to more frequent and severe illness. It's a cycle that keeps building.
"We're pretty sure that it's this sort of illness that will take him from us over time."
A letter from Starship outlining the decision not to offer life support again said: "It would appear from the information provided that William will suffer progressive respiratory decline as a consequence of his neurological injury ... it is the opinion of the medical practitioners working in the Starship Hospital intensive care unit that mechanical ventilation would service to prolong his death and potentially subjects him and his family to prolonged suffering."
The letter said taking William to Starship's intensive care unit would be the wong thing to do, and emphasis should instead be put on making him comfortable and ensuring extended family were with him if a severe repertory illness struck again.
The Burtons are considering their legal options, including seeking an immediate injunction against the decision, should that be required. Further action is possible too.
"I think, from what we've heard, you can challenge the hospital's decision and ask to get them to provide full support," Mr Burton said.
"We are thinking about it and we've started to do some investigation. The news is pretty recent and still pretty raw - within the last two or three weeks we've had the news."
The family is getting ACC support after filing a treatment injury claim.
The Health and Disability Commission has investigated what happened and its report is due for release today.
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The family has also set up a Givealittle page.
