At what point in History did women start successfully giving birth and retaining their child more often than not? What medical advances led to this? I’m sure I could google this but I figured an answer on here might be more thorough — Thanks!
This is a difficult question to answer, due to your assumption that infants and mothers, at one point, were more likely than not to die in or very soon after childbirth. This is a common stereotype of preindustrial Europe, but it's not quite true.
Rates of maternal and infant mortality are not easy to calculate with any kind of certainty, due to a lack of consistent and specific records. However, from examination of the records that do exist, historians have come to some conclusions. Edward Wrigley found that 12-20% of children died in infancy in the sixteenth through eighteenth centuries in one rural English village, a figure that's similar to what researchers in other areas have found; early modern women seem to have had a mortality rate in childbirth of about 1.3% (that's per birth - obviously, the more children a woman had, the worse her odds got). While these rates would improve greatly over the course of the nineteenth century, infants and mothers were still more likely than not to survive infancy/childbirth.
I'm not sure if you want to shift your question to be about improving maternal mortality rates during and after the Industrial Revolution (disregarding the "more often than not," basically), or if you actually want to ask about a potential prehistoric shift? I can do the former, but the latter might be more of a question for /r/AskAnthropology, though they might also say that there was not a point where this situation existed.