To find Clancy guilty, jurors had to be unanimously convinced beyond reasonable doubt that she intentionally killed her children and that she did not do so as a result of postpartum psychosis, a rare and serious condition.
The jury - nine women and three men - considered a range of options including not guilty by reason of insanity, manslaughter and first-degree murder.
Several jurors have said following the mistrial being declared that the panel was ultimately divided 11-1 in favour of finding Clancy not criminally responsible.
Another juror told local CBS station WBZ-TV that most of the jurors had been "very firm in their stance" from the start and "the stand-alone juror was not the only one that was unwilling to see things from the other side".
But they added that because Desronvil would not "follow" his reasonable doubt nor offer logical reasoning for his position, they felt Clancy had not received a fair trial.
Under Massachusetts law, prosecutors had to prove beyond any reasonable doubt that Clancy was criminally responsible for the jury to find her guilty. The defence did not have to prove her mental illness or lack of criminal responsibility.
He said the holdout "would not apply the law of reasonable doubt" as instructed by the judge, adding: "That's not right. And that's why I was upset."