I dont know about the US but here in Oz we were able to operate flights until 28 weeks pregnant. Did this with both my pregnancies and did not have a problem. Think it really depends on the pregnancy. Maybe some high risk women would be safer not too, not because of any risk from flying but that their pregnancy may be tenuous anyway. A normal healthy woman can do nearly anything pregnant. The baby is extremely resiliant. I actually went to Disneyland and took all the rides whilst in early pregancy. If the lady invovled doesnt feel right about it, dont do it. Hope this helps.