Should a Woman be allowed to abort her pregnancy at 9 months ?

I agree with Taliesin, no women electively aborts that far into pregnancy because she suddenly decided she no longer wants a baby or because she's too scared.
Inductions (because at that point a mother has to give birth to her child) it is because a severe defect has been found in the baby or mother.

The mother goes through birth and she is allowed to spend what little time her child has left to live in her arms. This is a difficult and horrible experience for any mother.
In many states abortions are no longer offered (electively after 20-24weeks: mostly 24) which is when a baby reaches viability.

Babies born at 24w without any serious defects or complications have a chance at survival with intensive medical intervention.

Babies who have some serious birth defects like trisomy 13, 18, or 21 may not be able to survive even when reaching term, most babies born with trisomy 18 die during birth or their first year of life. There are very very few who survive and of those who survive most of them are girls. All of the options and scenarios from worst to best as discussed with both parents any time something like that is found and especially if testing like amino gives a 100% answer. No mother takes this option if there is a slim chance the baby is ok.

Some mothers choose to continue the pregnancy until their baby passes naturally (the baby will suffer greatly) others can't go through that. Some babies become distressed in the womb because of their defects and endanger the mothers life.

In my opinion: To summarize elective abortions should not be done post 24w on healthy babies. After that point if a mother no longer wants her baby she can put the baby up for adoption.

Medically necessary abortions that place the mother at risk when a baby is not viable should remain an option.

Medically necessary inductions and deliveries post 24w should be available in state of the art facilities where intensive medical care is available to the child and mother to provide life saving alternatives to death in utero or death in delivery to mother or child.