exasperation
A feeling of being very annoyed and out of patience.
Exasperation is the feeling of being extremely frustrated and annoyed, usually after something keeps going wrong or someone keeps making the same mistake despite your efforts to help. When a parent asks their child to clean their room for the fifth time in one day, they might throw up their hands in exasperation. When your little brother keeps interrupting your homework to ask silly questions, you might sigh with exasperation.
The word captures that specific moment when patience runs out, not quite anger but definitely beyond ordinary annoyance. A teacher might feel exasperated after explaining the same math concept for the tenth time. A coach might shake her head in exasperation when the team makes the same defensive mistake in every game.
You can hear exasperation in someone's voice when they say, “How many times do I have to tell you?” or see it when they rub their forehead and take a deep breath. Exasperation is that worn-out, fed-up feeling when you've tried your best but the problem just won't stop.