nevertheless, long plane rides are often avoided during pregnancy. .
Doctors generally advise pregnant women to avoid flying during the third trimester. Not so much to prevent pregnancy problems, I think, but because of the risk of delivery. Delivery is sufficiently possible in the last trimester to make it a big enough risk.
In fact, I know of two stories of deliveries on planes. The first was a few years ago on a flight from Chicago to Indianapolis. Nominally, it's only like a 30 minute flight, if that, which is why I'm sure she had permission from the doctor to do it. Nonetheless, she delivered, and the doctor that did it was like a resident at the time.
It also just happened last Thanksgiving, on a flight from I think Chicago to Salt Lake City. She was only in her 7th month, and they diverted into Denver. I heard an interview with the doctor that did the delivery (these are always extremely touching stories).
The biggest problems these days with deliveries on planes is that there aren't any scissors to cut the umbilical cord. There might be a blood pressure cuff and a stethoscope, but that is about it. I know last Thanksgiving, that the doctor used shoe strings to tie off the umbilical cords and they found something sharp to cut it.
An interesting thing about these stories is that in neither of them do the doctors actually know the names of the patients. Last I heard, the doctor from last fall still had not been contacted by the family at all.