Lawyers representing a doctor investigated following the deaths of two babies are calling on her employer not to sack her after a judge this week refused to grant an interim injunction because the hospital's processes had "so many apparent holes" he could not foresee its board dismissing her.

The neonatologist sought to extend an interim injunction constraining Victoria's Royal Women's Hospital from dismissing her until after the Federal Court determines whether it breached the enterprise agreement when it launched an investigation after the death of two babies in 2015 and last year.

But Federal Court judge Tony North on Monday refused to further restrain the hospital's board from acting on a recommendation by the chief executive and chief medical officer to dismiss her.

Instead the hospital undertook to give 48-hours' notice before terminating her employment and agreed to participate in mediation ahead of a further hearing on August 23.

Barrister Craig Dowling argued on the neonatologist's behalf that there was "real risk" the board would dismiss her based on the recommendation when it meets in the middle of next month, with this and the criticism expected to accompany the dismissal likely to cause "irreparable harm even if later reversed".

In contrast, interlocutory orders delaying the decision until after the court determines whether the hospital's investigation process breached the AMA Victoria – Victoria Public Health Sector Medical Specialists Enterprise Agreement 2013 would cause her employer no inconvenience, Dowling said.

However Justice North said restraining the board in this fashion was "sort of a vote of no confidence in people who I will expect to do the right thing", whereas if they read the external report "like I can and without having medical knowledge" it would be "perfectly clear that it's a report of very limited value".

Judge criticises flawed investigation

Among problems with the hospital's investigation process, Justice North said there was a "pollution that comes" from having the neonatal medical director sitting on the first internal investigation given a background of unresolved personal difficulties between him and the neonatologist.

This contamination would be "difficult to wipe out unless one really takes care to insulate the next step", when an external reviewer was brought in, he said.

Justice North also criticised the external reviewer for observing that the neonatologist's actions might have contributed in one case, without describing "what they are, how serious they were", and he said "the fact is, they seem not to have been such that it would have made a difference".

Regarding the second death, he said the external investigator's report contained "vague allegations of lack of communication, never particularised by reason of who, when, where".

Following the external investigation, Justice North said the chief medical officer made a recommendation to the chief executive that "as I can see at the moment, completely misrepresents the background that I have outlined".

He said the chief executive's position became "Well, I have lost confidence. We don't know quite why" and "with all these doubts and she then activates the board".

Dismissal would be "surprising"

Justice North said it would be "surprising" if the board acted on the recommendation if it was "properly put in the picture", given also the neonatologist's 10-year tenure with no past issues to "cause a sudden loss of confidence" and the likelihood the board was comprised of "one hopes, people with independent mindsets".

When the "substance is appreciated", Justice North said there were "so many apparent holes in the [investigation] process that I couldn't imagine that there is, at the moment, a real risk" they would act on it.

He also noted that the neonatologist suffered from depression and said there was "no evidence" the hospital assisted her through the process or her illness "in order to bring her back to health and work.

Suggesting that this was "really is something to be investigated itself", Justice North said "long gone are the days when employees with this type of problem are just told 'Go home, take an aspirin and come back when you feel better'".

Maurice Blackburn Lawyers principal Josh Bornstein yesterday called on the hospital board to carefully examine the transcript of the hearing before deciding on any action.

"Our client is concerned that the whole process has been triggered by a complaint made of inappropriate behaviour in the workplace, and that no support was offered to assist in managing depression in a highly stressful and demanding role where difficult life and death decisions are made on a regular basis," Bornstein said.

"We call on the hospital to abandon this flawed and unfair process and resolve any outstanding issues so our client can restore their health and get back to their important work in the health system."

The Royal Women's Hospital declined to comment.