You need to have enough milk for the baby. If the baby is a Human or a moot, the baby will always disappear as it acts as a extra life, you re-start the game with the same level and bank contents if you die (I am guessing it's the work of the fortune teller, judging from her dialogue when you re-spawn and if you kill her). If I had to guess, you can only keep the second+ Moot/Human baby but i'm not grinding through 2 pregnancies to check.
You get to keep goblin, orc-kind, fish-kind, deep-one, and infestation babies though.