I had an undiagnosed circumvallate placenta and our baby died in utero at 37 weeks. There are no guarantees that just because you've gotten that far, you're safe.
I feel that the statement "The chances of a healthy birth increase with each week that the woman can successfully carry the pregnancy" is false hope. Even though I had proper medical care and higher level ultrasounds (one even days before our baby died), there is nothing short of delivery that can ensure your baby will take its first breath, open its eyes and cry. Stillbirth happens a lot more than anyone talks about until you cross over into the baby loss side of parenting.