Some airlines say that they don't allow a pregnant woman to fly if she's already in her 3rd trimester. But I've heard stories of a friend of a friend (of a friend...) was able to board a flight to Manila and so on and so forth.

Now my firsthand experience (my wife that is): She travelled from Doha to Manila last year during her 2nd trimester. Qatar Airways gave me this form to fill up and had to be signed by a doctor. After that its all clear to the airport.