Some people would argue that it was when Jasnah's father, King Galivar, was slain by the Assassin in White that she broke. I, however, disagree on multiple points.
The quote below suggests something that could contribute to her breaking. This is right after Jasnah uses her soulcaster to kill the thugs.
Breaking is a gradual process. It wasn't when Tien died, or when his spear-squad was slaughtered, or when he was betrayed by Amaram, or when he failed to save some slaves, that Kaladin broke, it was all of those instances together.
Her father being killed may have tipped her over the edge, but something most likely happened before that.
What do you think happened?