The High Court on Friday deferred the trial of Major Peter Mwaura Mugure.
The case has now been postponed to January 10, 2020.
Mugure is the prime suspect in the murder of his estranged wife Joyce Syombua, her 11-year-old daughter Shanice Maua and her son Prince Michael, 5.
The plea-taking session has now been cancelled for the third time. This is after the state counsel said that the accused is not in a position to respond to questions in court because of his health condition.
State Counsel told the court that the medical report of the suspect had not to be presented before different parties, which made it difficult for them to proceed with the case.
Senior Assistant Director of Public Prosecutions Peter Mailanyi confirmed that the suspect had been taken through the medical examinations. He, however, said that the psychiatrist had refused to compile the report after the test was conducted.
Attempts by defence lawyer Cliff Ombeta to contact the mother of the suspect proved futile. While representing Ombeta in court, Lawyer Wanjiku Muguro said that the mother refused to travel from Nairobi to Nyeri to testify in court.
"I will be seeking further instructions from Mr. Ombeta. He has been trying to get in touch with the accused’s family," Muguro said.
Bodies of the deceased were found buried in shallows graves in Nanyuki before the suspect was arrested.