Looking on the web for some demographic data, I find:
"Some historians have estimated that up to a quarter of infants born in Medieval times died before they even lived for a full year."
again in Middle Ages, "infants and children died at a horrific rate (some say up to 1/3 of all died before the age of 5)"
"These figures include the high number of infants who died within days after birth from little-understood and wholly unpreventable illnesses that modern science has thankfully overcome."
I have no precise figures but trying to infer approximate values from easily available data :
Taking the period of 1000 years of the Middle Ages, assuming an average population of 60 millions in Europe (300 millions in the world), renewed at a speed of 3-4 generations per century, we get about 200 milllion adult lives per century, but for each 2 people reaching adulthood there was 1 dead baby or child. This gives a total of about 1 billion dead European babies or children in 1000 years (or 5 billion total in the world).
And most of these deaths happened against the mother's will.
It's not their mothers who killed them. While abortion can be a tragedy for the baby, who can say how worse may this really be compared to a forced survival in a society trying to forbid abortion, as if a prohibition was practically possible without lots of troubles and risks of circumvention, and as if the mother was not often the right person to weight her responsibilities, between her mother's instinct attached to the child's life and her responsibility of growing him in hard circumstances ?
But while things may be debatable in the case of unwanted pregnancies of mothers looking for abortion, isn't it much clearer that a child needs to be saved when the mother does want the child to survive ?
And why did they die : quite often, that was due to poverty and bad medical care at a time when basic concepts of medicine and infectious diseases were not understood yet. Note that this didn't come from sin : people did not want to kill, nor to disobey God. They devoutly prayed God to save the child, but could not hear any response. God wanted them to do the right thing to save the child, while they did want to hear that tip, but they could not.
Definitely, they wanted with all their hearts to hear God's avice how to save the child. They just could not find anyone to hear and report this advice from God.
Who was responsible for this ignorance ? Clearly, is guilty anyone who was able to hear that so much needed information from God and report it to the people but refused to do so. And in all history, there is mainly one person who commited that crime, and that is Jesus. Because Jesus was the one in position to hear from God any message He had to say, and to report it to the people; it would have sufficed to benefit all Europe and beyond in a couple of centuries, through the audience that his message was about to have, thus ultimately saving about 1 billion children from premature death. By the way, as such a revelation would have been a much clearer evidence of his divinity than we had, it would also have helped spreading the Gospel better (both as an argument and by demographic pressure), thus saving the need of a few wars against disbelievers to convert them.
Now, apart for Jesus, can we find another big culprit ? Yes we can : according to wikipedia, "Among women who know they are pregnant, the miscarriage rate is roughly 10% to 20% while rates among all conceptions is around 30% to 50%". Who is the culprit for this ? Again, not the mother. The one person guilty of having so badly designed the human body functions so as to lead so many babies to death even before being born, is God the Father.
we have the 2 main culprits on one side, who or what can we find
on the other side as the best baby savior ? The main ones turn out
to be the progress of medicine, and also, modern science and
economy, which got so many people out of misery. Strangely, no
word about the high value of these things for such concerns can be
found in the Bible; and the scientific progress which was about to
drive this, and which was well on its way until the end of
Antiquity, got mysteriously stopped for the 1000 years period of
the Middle Ages, a period whose start roughly coincided with the
Christianization of Europe. God knows why.