According to American Sniper screenwriter/executive producer Jason Hall, there’s actually a good explanation as to why fake babies were used on the film. In response to journalist Mark Harris’ tweet “That plastic baby in American Sniper is going to be rationalized by Eastwood auteur cultists until the end of days,” Hall replied: “hate to ruin the fun but real baby #1 showed up with a fever. Real baby #2 was no show. (Clint voice) Gimme the doll, kid.”
http://www.hollywoodreporter.com/news/american-snipers-fake-baby-mocked-764702
Yeah, the story I heard was #2, that they had two babies ready to film, and one was sick and one didn’t show up.