An out-of-court deal that would have seen Justice Kalpana Rawal automatically step in as acting chief justice flopped on Friday after the JSC rejected it.
The commission refused a deal allowing Rawal to remain in office until end of the year, saying it has no mandate to extend judges' retirement age.
Rawal is challenging the Court of Appeal's decision that she retires at the age of 70.
"The retirement age of judges is a constitutional matter that is not negotiable," the Judiciary Service Commission said in a statement sent to newsrooms.
It noted that the matter has been heard and determined by 12 judges of the Superior Courts.
The judges - five in the High Court, and seven in the Court of Appeal - unanimously determined that the retirement age is 70.
The intended to allow Rawal to serve until December 31, 2016, after which she would receive a package calculated to the age of 74.
LSK also suggested that Justice Philip Tunoi be allowed to stay in office, pending the investigating a Sh200 million bribery claim against him.
But the president of Law Society of Kenya Isaac Okero told the press on Friday that he remains optimistic, and the talks will continue.
He met with JSC members at the Supreme Court, with exception of Chief Justice Willy Mutunga and Justice Smokin Wanjala.
The two are part of five-judge bench hearing .
JSC members who attended the meeting were Mohammed Warsame, Aggrey Muchelule, Emily Ominde, Tom Ojienda, Margaret Kobia, Githu Muigai, Winnie Guchu, and Kipngetich Better.
LSK had made the but no resolution was met during the process.
The case continues on Monday.