Why not order a new trial?
The primary ground by which she was found guilty at the first trial was, as I have said, a now discredited medical theory that told the jury the odds of all four children dying young was on the order of a trillion to one.
That was the primary piece of evidence that lead to her conviction. And it’s now known to be nonsense.
Why not order a new trial? Most likely because she’s served most of her minimum sentence already and because there is a general view, now supported by the prosecution as well as the defence, that, at the very minimum, reasonable doubt exists as to her guilt, which means the prosecution would not be willing to proceed with the case (if a prosecutor decides reasonable doubt exists, they will generally not take a case to court).
Sorry - just realised you are referring to the first inquiry, not the trial, which I’ve referred to.
At the time of the first inquiry in 2019, only the two girls had been identified as having genetic abnormalities. That fact reduced the statistical likelihood of all four deaths being non-suspicious substantially, but the Judge in that case, concluded it was still so unlikely as to not constitute reasonable doubt.
It’s only since then that the genetic issues in the case of the two boys have been identified, which has lead to a much higher chance of all four deaths being non-suspicious.