The jury deciding the verdict for murder in the marathon trial of David Harold Eastman told a court on Monday they have been unable to reach a unanimous decision.
Acting Justice Murray Kellam encouraged the jury to continue deliberating for a time before he sent them home early for the day, saying: "I don't want anyone suffering from stress."
The jury had begun their discussions at about 10.30am on Wednesday.
Mr Eastman, 73, has pleaded not guilty to murdering Australian Federal Police Assistant Commissioner Colin Winchester at about 9.15pm on January 10, 1989.
Mr Winchester was shot dead as he pulled into his next door neighbour's Deakin driveway on that date with two shots to the head.
His trial began on June 4 this year with a jury empanelment at Albert Hall.
During the trial, prosecutors alleged Mr Eastman was motivated by a murderous hatred of police and was the one who killed the police chief in 1989.
They said the murder weapon was a Ruger 10/22 sold by the late Louis Klarenbeek, and alleged a witness saw Mr Eastman at the gun seller's home.
There were too many coincidences for Mr Eastman to not be the killer, prosecutors said.
But the former treasury official's defence team said there too many unknowns in the evidence. They argued that it was not Mr Eastman who bought the murder weapon.
The defence also pointed to what they said was a reasonable possibility that the Italian mafia orchestrated a hit on the senior police officer, believing he had betrayed them.
The jury retired to begin deliberations about 10.30am on Wednesday, and went home for the weekend before returning on Monday morning.
During their deliberations, they asked the court for access to transcripts including of the evidence of Mr Klarenbeek, his wife, and that of Denis Reid, and Raymond Webb.
Mr Reid gave evidence in the trial that a man he said was Mr Eastman had come into his Queanbeyan sports store and tried to sell him a Ruger 10/22 shortly before the murder.
The Crown case is that the sight of the Klarenbeek Ruger was off.
Mr Webb had told the court that he saw Mr Eastman going into the Klarenbeek home.
On Monday, the jury sent a note to the court saying they had been unable to reach a unanimous verdict and asked the judge for advice.
The judge called the men and women back into court at about 12.30pm, where he said he did have the power to discharge the jury if there was no genuine likelihood of them reaching agreement.
But he said experience showed that with more time sometimes agreement could be reached.
Acting Justice Kellam encouraged the jurors to re-examine the points on which they disagreed.
But he also warned the jury members that if they could not honestly agree, they must give effect to their own view of the evidence.
The jury retired again briefly before the judge called them back in at about 2.30pm to send them home early, saying it had been a long day.
The jury is expected to return on Tuesday to continue deliberations.