When Characters Can't Take It Any More

On the "Acknowledgments" page at the beginning of the book Eragon, author Christopher Paolini thanks his family, the editors who helped him with the book, you know--all the usual people. But then he also gives a 'thank you' to his characters, for bravely enduring all the things he puts them through. It made me smile.
We writers really do put our characters through some horrible stuff, don't we? And the experts are always telling us to take it up a notch, to increase the drama and tension and misery until we've driven them absolutely to rock-bottom. Fair enough. After all, what good is a story without drama? What good is a hero/heroine who doesn't have to struggle and fight to become the hero/heroine?
But our characters are human too, and a person can only take so much before emotions start getting backed up in the system and they've got to come out sometime... especially if the character in question is a girl. The result is what my mom would refer to as a 'meltdown'. (By the way, best meltdown ever: Rapunzel's little episode in the movie Tangled!)
Not too long ago, I read somewhere that in most cases your heroine shouldn't cry more than once over the course of the story. I understand the sentiment behind that statement--no one wants to read about a character who's so weak emotionally that she breaks down and sobs over everything--but still, I'm not sure I entirely agree.
I'll use one of my stories as an example: if I were to allow the heroine to cry only once over the course of this particular story, I would have to make some very tough decisions. Should she cry when her whole life's dream is ripped out from under her, or should she save it for when she loses the only family she has left? What about when one of her country's soldiers, whom she has been friends with for years, dies in her arms? Or, should she wait until her country is invaded by a demon-possessed army and she is forced to flee? Which of these events can she not cry over without seeming utterly cold and heartless?
I don't doubt that if I wrote in a huge emotional ordeal for the heroine following each of these events, the pages would begin to get soggy and readers would lose interest. But I don't think I'm going to take it so far as to allow the heroine only one round of tears over the whole story, either. My goal is to get a good balance of realistic tears when circumstances call for them, but only one big 'meltdown': that pivotal, rock-bottom moment that changes the course of both the story and the character's arc.

What are your thoughts on character meltdowns? How do you balance piling on drama and misery with keeping characters' emotions under control?
Anybody have a favorite fictional meltdown?