Appeals aren’t meant to be a redo of the original trial. The judge ruled that he didn’t prove he was innocent, or that a reasonable juror couldn’t have voted to convict him if they saw his new evidence.

Please explain how "expert testimony has been widely discredited" doesn't count as new evidence?

It’s new evidence, but it doesn’t contradict the entire case. In particular, there are witnesses who said they saw him abuse the kid in the past, and child abuse remains a real thing regardless of medical disputes about whether there’s a distinct “shaken baby syndrome”. So the judge felt that a reasonable juror could have convicted him even in light of the new information.

I don't presume to know this case. I was replying to what seemed like a characterization of the medical testimony in this case as belonging to the latter group, when in fact it has been shown over time to be as invalid as the former.

There ceased to be a distinction between the two groups in your original comment when the weight of evidence started to clearly tip away from prosecutions like these.