Detective Constable Steve Leonard of Hastings Police said Kairau had been recovering since his release from hospital on October 20.
There was a warrant to arrest for a 14-year-old boy in relation to the incident.
The boy was actively avoiding police and it was believed friends and family were helping him hide.
Police were determined to track him down, as well as three others believed to be involved.
"This was an unprovoked, cowardly and vicious assault and we are determined to find the person responsible," Leonard said.
Leonard was urging anyone who knew who the boys were, to get in touch.
Kairau's mother Lisa said her son had been recovering well since being released from hospital.
When he first got home he had been suffering from bad headaches and memory loss due to a brain injury and it was unsure if he would have any long-term effects.
However, his headaches had subsided and his memory loss was slowly getting better.
A concussion specialist had told Ms Kairau that Ayden should make a full recovery.
"He said he feels a lot better, he's healed a lot," she said.
"Physically he is pretty much back to normal ... the memory loss is still there but it is something we are trying to cope with."