Yes. They break when they flex. Don't mind my crude drawing I'm about to make here, but this should hopefully explain why they break:
Picture your swaybar like this, when the rear end isn't moving side to side:
|________|
When it moves, you get this, as it trys to move with the rear end housing, when the control arms flex:
\________\ or /_________/
Eventually the metal fatigues and breaks. The panhard bar will eliminate the rear end sway, so the swaybar should be safe from breakage at that point.