NO they are not supposed to but you know how many people are - it only happens to the others......... On longhaul flights it is often embassy staffers who fly "home" to have their baby there. We had one on our Korean flight early this year tooo and I had to wonder just why women take these kinds of risks with their babies. The current rule is 27 weeks but many cruiselines are starting to reduce those requirements to 25 weeks (based on the fact the premature babies in the good prenatal unit with can survive at 25 weeks) THAt sort of help is just not available at 35.000 feet or at sea.
One of the babies born on a LH flight (also am embassy staffer) has the flight number and the exact position as recorded by the capt. as place of birth in her passport. Lufthansa is also her "Godparent"