Chief magistrate Heston Nyaga granted the police more time since the suspect has been in hospital for six weeks.
" Since the matter is of public interest, I allow the prosecution's application to complete their investigations", Nyaga ruled.
The new investigating officer Oliver Nabonywe had requested for a day to be able to get Nyakundi's finger prints, visit the scene of crime and interrogate him more.
Nyakundi was expected to appear before court on Wednesday but failed to show up.
Investigating officer Godfrey Munene said Nyakundi was still sick.
He said investigations were not complete because he needed some verification from Nyakundi after he is discharged.
Last week, the investigating officer told the court Nyakundi had recorded his statement in hospital.
Munene said Nyakundi was still in hospital because his condition was fluctuating.
Nyaberi told the court his client was still receiving treatment but was in a fair condition.
“My client is getting better and might be discharged when he gets well,” he said.
The case will be mentioned on May 7.
Munene on April 4 told the court that he had been unable to record a statement from the "incoherent" lawyer.
"I visited the suspect and I can confirm that he is still sick and will need more time to see if I can record his statement," Munene said.
Nyaberi said, "My client is unwell as his condition keeps on fluctuating. His blood pressure is high and he needs to be in the hospital but I am willing to go with the investigating officer to the hospital to get Nyakundi's statement."
The city lawyer is accused of killing his son, Joseph Nyakundi, on March 17. He was admitted to Nairobi Hospital under guard after the shooting.
Joseph was buried on April 2 at Lang’ata Cemetery.