Regarding problems of producing royal offspring, I always liked the rumored story of how Louis XIV was conceived: after his mother Anna of Austria had experienced four stillbirths and failed to produce an heir, she fell in disgrace and was largely ignored by the king. On December 5th 1637, after 23 years of a marriage that at that point only existed on paper, the king was on his way to a hunting lodge near Versailles. Bad weather forced him to stop at the Louvre palace, where his wife was already set up for the winter. The only rooms that were heated were hers, so the king was forced to share a bed with his wife. 9 months later, on September 5th 1638, Louis XIV was born.