The $100,000 reward for information on the person responsible for murdering Arthur Easton, will expire in 7 days.
Easton was killed after an intruder entered his Papakura home in Auckland nearly four decades ago.
Police announced the reward in October last year, which will remain in place until midnight on 24 January.
It was offered for a limited period of three months to encourage people who have credible, current information to come forward now, and not leave it any longer, police say.
On Sunday 13 October 1985, a male intruder entered the Easton family home on Grove Road at 8pm.
Police say Arthur and his two teenage sons confronted this offender in the hallway, which lead to a violent altercation and ultimately the death of 52-year-old Arthur.
Detective Inspector Adkin said it was not too late to come forward and give Easton's family the answers they deserve.
"We cannot provide details while the investigation is ongoing, but we are committed to getting a result as soon as possible," Adkin said.
"We are determined to find the person responsible for killing Arthur and we know there are still people who have not yet spoken to police and who may have information about the events around Arthur's death."
Easton's death led to the wrongful conviction of Alan Hall, whose conviction was overturned in 2022. Three people charged with perverting the course of justice during Hall's case will go on trial in 2026.
In the family's first public statement, in December, Easton's son Patrick said the family knew there were people who had knowledge that could help.
"We are here to ask for help, and to get justice for our father," he said.
"He taught us to always do the right thing and he would have loved to see and be part of the lives of his eight grandchildren and soon to be five great grandchildren."
His father's death had "sucked a lot of joy out of our lives", he said.