Loss of child as punishment?

It is not easy to decide whether to send a mother that has left her child in a car in the summer to jail or not. Honestly, I'm not even sure what I would do if I were the judge.
Obviously the mother did not kill her baby on purpose, or wanted him any harm. Not only did she lose her child, but even worse, it was her own fault, and she will have to deal and live with that guilt for the rest of her life. Therefore I understand why some people think that an additional punishment is not necessary
On the other hand, however, being a mother involves a lot of responsibility, which the mother in this case obviously lacked. How could you possibly "forget" about your own child?? How much attention do you pay to your child if you don't notice it in your back seat? Looking at it from this perspective, the mother committed a crime; because an infant is absolutely helpless, it relies on its mother. However, the mother in this case failed in her "job" as a mom. If a mother cares so little about and for her child to simply forget it was in the car, she shouldn't even be a mother, and deserves punishment.
After all I think there are good arguments to sentence a mother like that to jail time, as well as not to. However, I think the police should also research whether the woman was usually a good mother, or if there had been more incidents already.