The jury in the US trial of Lindsay Clancy returned to court on Wednesday to try again to reach a verdict in the deaths of her three children.

The panel had told the judge a day earlier they had been unable to agree after days of deliberations and were instructed to keep trying. Clancy, who has pleaded not guilty, faces three counts of first-degree murder.

Prosecutors have alleged that she made a calculated, intentional decision to kill the children in their Massachusetts home in 2023.

Her lawyer does not dispute Clancy killed them but says she was suffering from postpartum psychosis and was unable to distinguish right from wrong – meaning she should not be held criminally responsible.

The jury began deliberating on Thursday after hearing weeks of testimony from dozens of witnesses. The panel returned to the courtroom on Tuesday, after telling Judge William Sullivan they were deadlocked. The announcement drew audible gasps in the courtroom.

He instructed them to keep trying.

Clancy, a 36-year-old former nurse, appeared stoic as she sat in a wheelchair beside her lawyer. She was left paralysed after jumping from a second-floor window after the killings.

It is not uncommon for jurors in high-profile trials to struggle to reach a decision, and judges have protocols for such situations.

A deadlock among the jury such as this one happens in “complex and emotionally charged trials”, Heather Cucolo, a New York Law School professor and expert in mental health law, told the BBC.

Although jurors have not been provided a specific deadline, there is a limitation to the number of times that a judge is expected to ask them to continue deliberating. If they say a second time that they are at an impasse, the judge has a new recourse.

“If the deadlock persists, the judge might issue an additional ‘dynamite’ instruction [known as a Tuey-Rodriguez charge in Massachusetts] to encourage the group to consider alternative perspectives and strive for an agreement while upholding their genuine convictions,” Cucolo said.

But it is “typically a last-ditch effort” from a judge, she said.

If the jury reports that it is deadlocked for a third time, the judge could declare a mistrial.

Criminal defence lawyer Elyse Hershon told the BBC she was not surprised to hear that the jury was deadlocked, as people had strong opinions on the case.

“The facts are difficult and a lot of the evidence is graphic so they have a lot weighing on them,” she said.

The five-week trial in Plymouth, Massachusetts, has generated significant public interest and crowds have sometimes gathered outside as hearings take place.

A woman was arrested on Tuesday by state police outside the court building, Massachusetts State Police confirmed to the BBC. She was expected to be charged on Wednesday with “intimidation of a witness, jurors, or person furnishing information”.

Police did not give any further information, and it was not clear whether the incident was connected to the Clancy trial.

Clancy is accused of strangling her kids – Cora, five, Dawson, three, and Callan, who was eight months – with fitness bands in their Massachusetts home in January 2023.

The defence argues that Clancy was experiencing postpartum psychosis – a severe mental health condition that can develop after childbirth – and that for this reason she should therefore not be held criminally responsible for the killings.

If she is found guilty of first-degree murder, the intentional and premeditated killing of another person, Clancy will face a mandatory life sentence in prison without the possibility of parole.

She could also be found guilty of a lesser charge, including second-degree murder – committed with malice or extreme recklessness, but without prior planning – or manslaughter – unintentionally killing “by wanton and reckless conduct”. In either of those instances, she would face time behind bars.

If Clancy is found not guilty by reason of insanity, she will not be set free – she would instead be sent to a psychiatric hospital where her status would be periodically reviewed. She could stay in hospital for the rest of her life.

If you are suffering distress or despair and need support, you could speak to a health professional, or an organisation that offers support. Details of help available in many countries can be found at Befrienders Worldwide: www.befrienders.org, external.

In the UK a list of organisations that can help is available at bbc.co.uk/actionline.