A pregnant woman can be counted on to go into labor at the least convenient time possible.
Alternately, "Murphy's Law of Pregnancy". If a woman in fiction is established as near-term pregnant, and there comes an event that would be the worst possible time for her to go into labor, the baby is going to pick that time to be born. Doesn't matter if its drama or comedy, doesn't matter when the baby was actually expected to be due, doesn't matter if The End of the World as We Know It is approaching - it's coming now and the cast is going to have to deal with it on top of whatever crisis plagues them. The most common exception, oddly enough, is any episode where the mother is already expecting to go into labor any moment and the drama around the birth itself is the point of the episode. Super Trope of Born in an Elevator. Frequently calls for a Delivery Guy and involves a Screaming Birth.