The jury has been deadlocked 11-1 with the majority apparently leaning towards finding the 36-year-old Clancy not guilty by reason of insanity.
The dramatic developments came after the jury sent a note to the judge Friday morning saying that it was with a "heavy heart" that they were unable to reach a verdict in the case, which has cast a spotlight on maternal mental heath.
Clancy does not deny strangling Cora, five, Dawson, three, and Callan, eight months, but claims she was suffering from postpartum psychosis -- excusing her from criminal responsibility.
To reach a verdict, all 12 jurors must be in agreement. If they cannot agree, the judge declares a mistrial and prosecutors must decide whether to try the case again with a new jury.
Kevin Reddington, Clancy's lawyer, has repeatedly demanded the replacement of the holdout juror with one of several alternate jurors but Sullivan declined to do so.
Clancy's televised five-week trial, which featured more than 80 witnesses and days of distressing testimony, has sparked debate in the United States over maternal mental health.
Clancy has pleaded not guilty by reason of insanity, saying she heard a voice ordering her to kill her children.
Her lawyers say this was caused by postpartum psychosis, a condition that experts say affects about one to two women in every 1,000 births.
Prosecutors have rejected that argument, saying Clancy had carefully planned the murders of her children and was able to understand the consequences of her actions.
Psychiatrists and people close to Clancy, as well as her estranged husband, were among the witnesses who testified about her fragile mental health during the trial.
'Lousy medical care'
Dozens of women dressed in pink have showed up at the court in Plymouth to extend their support for Clancy -- and to make a statement about women's health more generally.
During closing arguments, Reddington, Clancy's lawyer, said she had made numerous pleas for help before the killings but had received "lousy medical care" from the doctors she consulted.
After the murders at the family home in Duxbury, Massachusetts, in January 2023, Clancy jumped from a second-story window in an apparent suicide attempt that left her paralyzed from the waist down.
The former nurse faces life in prison without the possibility of parole if found guilty of first-degree murder.
Jurors can also find Clancy guilty of second-degree murder, manslaughter, or not guilty by lack of criminal responsibility -- a verdict that would see her confined to a psychiatric facility.
The trial has revived memories of a similar case that also captivated the country 25 years ago, that of Andrea Yates, a Texas mother who drowned her five children in 2001.
Yates was initially convicted and sentenced to life in prison, but she was found not guilty by reason of insanity at a 2006 retrial and committed to a psychiatric hospital.
