Three days after that, on William's third visit to hospital, meningitis was diagnosed and his parents, Derek and Wendy, then spent a heart-wrenching month watching their boy's brain wither away.
The DHB's investigation found the second doctor to see William did not give the possibility of an infection proper consideration and the hospital did not have in place a proper process for more senior staff having oversight of paediatric juniors.
The DHB has since changed its practices, including making sure a child taken to hospital twice within 72 hours is examined by a senior staff member.
The health board has also apologised to the Burton family. It will assess the changes it has made in six months' time.
"CCDHB remain saddened by the significant neurological injury and permanent disability that resulted following William accessing our care," it said in the commissioner's report.
The second doctor to see William was now overseas, but the board said: "It's difficult to convey in writing the distress and regret felt after hearing of William's neurological injury. I have been deeply affected by the outcome on William's health and cannot begin to imagine how affected the Burton family must be."
An independent paediatric emergency specialist, reporting for the commissioner, found William's care adequate on his first visit to hospital, but he was concerned the boy was only seen by a junior doctor on his second visit.
That doctor also didn't give the Burtons clear instructions about what to do if William's fever remained, but their assessment was appropriate given their level of experience.
In a statement, Capital and Coast DHB chief medical officer Geoff Robinson said the DHB accepted the commissioner's findings and "unreservedly apologises for the grief and distress suffered by the patient and their family as a result of this regrettable event".
"As health professionals, patient safety is our number one priority and we have taken several actions following this event to reduce the risk of it occurring again," Dr Robinson said.
"A formal assessment and discharge process for patients seen by junior doctors has been developed to ensure greater clinical oversight from senior doctors. Any child who re-presents to hospital within 72 hours is now assessed by a senior doctor before discharge.
"We have increased staffing to ensure a paediatric registrar, a doctor who has at least three years' experience, is on duty 24/7. All
Everything you need to know about meningitis
What is meningitis?
Meningitis is a severe illness caused by meningococcal disease. It is an infection of membranes that cover the brain and spinal cord. Meningococcal disease also causes septicaemia, or blood poisoning.
Who is most at risk?
Meningococcal disease can affect anyone, however, babies, children under 5, teenagers and young adults are most at risk. All babies under the age of 1, and Maori and Pacific children under 5, are most at risk.
How do I get it?
The bacteria are transmitted through droplets of respiratory or throat secretions, by kissing, sneezing or coughing. Basic steps like covering your nose or mouth when sneezing or coughing, and washing and drying you hands thoroughly, can help reduce the chance of spreading the bacteria.
Factors believed to put people at higher risk include living in overcrowded housing, exposure to tobacco smoke, and having a respiratory illness like the flu. It can be caught at any time of the year, but is more common in winter and spring.
What are the symptoms?
Symptoms may include a high fever, headache, vomiting or in infants a refusal to feed, confusion, sleepiness, a stiff neck, a dislike or sensitivity to bright lights, joint and muscle pains, and a rash.
A rash consisting of reddish-purple pin-prick spots or bruises, that don't disappear when you press on them with a glass, is a very worrying sign. You should call an ambulance immediately if a rash like this appears on a sick child or adult. However, do not wait for a rash to appear before seeking medical help if other symptoms are being shown - one in three people with meningococcal disease have no rash at all.
You need to be alert to signs of meningococcal disease because it can come on very quickly. It is also difficult to diagnose, because it can look like other illnesses, such as the flu.
Can it be treated?
Meningococcal disease can be treated with antibiotics, but early treatment is very important. It cannot be treated at home - it is important to seek medical help immediately.
What should I do if my child has symptoms of meningococcal disease?
Call you doctor straight away, or call Healthline for free on 0800 611 116 at any hour of the day or night. If you have seen a doctor and gone home, but are still concerned, call your doctor or seek medical advice again. Don't be put off - insist on immediate action. Keep a close watch on the sick person, and do not leave them alone.
Can it be vaccinated against?
There are vaccines that protect against meningococcal disease currently available in New Zealand, but they are not publicly funded for most New Zealanders. The vaccines do not protect against all types of meningococcal disease - only strains A, C, Y and W-135. There is currently no vaccine available for meningococcal B.
None of the vaccines are long lasting. Even if you or your child have been immunised in the past you may no longer be protected.
(Source: Ministry of Health)