Elizabeth Vaughan tells of turning in a manuscript in which an infant died midway through. Her publisher sternly counseled her that "In romance, you can't kill a baby." She had to rework the entire plot to accommodate the infant's survival.
While the Pern colonists' first encounter with Thread gruesomely killed several adults and at least one young girl, Dragonsdawn does honor this trope with babies. Two infants were the only survivors of the colony's Tuareg nomad camp, having been sealed inside a Thread-proof metal cabinet by their doomed parents, and a house in which a woman is giving birth was instinctively protected by hundreds of the settlement's fire-lizards.
The very premise of Harry Potter, who is The Boy Who Lived because the evil overlord wanted to kill a baby but wasn't able to. "Trying to kill a baby but not being able to" is probably the most pathetic thing a villain can do. It's hard to think of things that couldn't kill a baby, but apparently Voldy just had to get cute with the Killing Curse, instead of using the much more reliable kick to the head.
In fairness to Voldemort, Harry is the only survivor in the spell's history and only because of a peculiar set of circumstances both times. Nobody, under the circumstances, could have expected failure - but the consequences for Voldemort the first time were such that he had no opportunity to rectify the situation.
Voldemort manages to kill two children (and their mom) while searching for a wand-maker in Deathly Hallows. Many teenagers die through the series, but only a few (Moaning Myrtle and Colin Creevey, plus Ariana Dumbledore in the backstory) were under 17, and thus minors.
Lampshaded up the wazoo by the Samurai Cat books, in which Shiro the homicidal kittenrevels in his Baby+ Cat Immortality, gleefully rushing into meat-grinder battles in the smug confidence that the author wouldn't dare kill him. Eventually this trope was averted in Samurai Cat Goes To Hell, but only as a plot device to send his uncle to retrieve the bloodthirsty little creep.
Played straight in Breaking Dawn. While all of the Volturi converge to kill Bella and Edward's daughter Renesmee, they all instantly become captivated by her charm when they see her, quickly realize that they were wrong, and go home without a fight. Yes, that was the climax.
Did you actually read it? Even after it was proven that Renesmee wasn't a danger, the Volturi still tried to find an excuse to kill her and thus provoke the Cullens AND they still started a fight...well, attempted to, anyway.
Averted by the Volturi. Their only reason for killing a little kid was because they don't give second chances.