Generally speaking, custody orders can't be disturbed without a material change in circumstances.
A mere diagnosis would not itself be a material change in circumstances and would also usually not be admissible evidence because of the doctor-patient privilege and related privileges for mental health professionals. A diagnosis changes the way people interpret a situation, but it isn't actually something involving or impacting the parent-child relationship in the life the parent and the children that has changed.
Instead, there would need to be some event or circumstance that was not known or contemplated at the time of the hearing giving rise to the original custody order which would undermine the factual basis or reasoning of the original custody order.
Assuming there are no allegations of abuse verbally or physically or
other new issues with the parent, how likely would it be that the
custody ruling would be changed?
The answer is never "zero" because judges in custody cases are inherently unpredictable. But the likelihood of a change is low.
Also, even if there was a prima facie showing of some change in circumstances, e.g. the parent with PTSD is fired from a job for having an outburst at work that a reasonable person would not have made but for PTSD, the diagnosis isn't necessary a negative.
A diagnosis followed by repeated incidents after which the parents makes no effort to prevent incidents like that from happening again might be a negative. But often a diagnosis is followed immediately by a treatment plan or the development of strategies to reduce the impact of the condition diagnosis that is informed by the diagnosis and hence likely to be more reliable and effective than efforts to deal with an undiagnosed condition.
If the parent is diagnosed with PTSD and then undergoes a treatment plan targeted towards advancing the best interests of the children, in ways that the same parent had not considered at the time of the original hearing, the diagnosis could actually be a plus. The existence of a treatment plan could reduce the significance of pre-diagnosis incidents that happened before a treatment plan was in place.
Indeed, probably the more common fact pattern would be for parenting to have been initially restricted based upon incidents which in hindsight were caused by PTSD. Then, the parent is diagnosed, starts a treatment plan, and shows that incidents like the ones that previously caused the court to limit custody are now no longer happening regularly. A court could treat the reduced frequency of incidents and the circumstance of treatment that suggests that the reduced frequency of incidents is not just a fluke, as a change in circumstances justifying less limited parenting time.