Lindsay Clancy just lost her recent bid to have the murder case against her thrown out … TMZ has confirmed.

New court docs, obtained by TMZ, show JudgeWilliamSullivandenied Clancy’s motion to find her not guilty of murder after the trial resulted in a hung jury. 

Her attorney, Kevin Reddington, argued in court earlier this week that the prosecution failed to prove she murdered her kids.

However, the judge found prosecutors presented enough evidence for a “rational” jury to “find beyond a reasonable doubt the elements of the charge of murder.”

The judge pointed to evidence showing Clancy was alone with her three children while husband Patrick Clancy was out picking up medication and takeout … with video placing Patrick at both stops around the time of the killings.

Sullivan also addressed Clancy’s mental state, noting experts on both sides agreed she suffered from serious mental illness … but disagreed over whether she still understood what she was doing was wrong.

Prosecutors presented three experts who said she did, while defense experts said otherwise. Sullivan said that disagreement is something a jury could sort out to reach a guilty or not guilty verdict, and the judge was not inclined to second-guess their determination.

So for now, the case stays alive.

As TMZ previously reported, Clancy’s first trial ended in a mistrial after the jury deadlocked 11-1.

Her defense has since shifted gears … arguing there wasn’t enough evidence to prove she killed the children at all, while also trying to block a retrial on double jeopardy grounds.