It's probably a layout issue to do with the current sense resistor. Breadboards are horrible when it comes to resistance and, especially, inductance.
I'd bet if you probe pin 7 with a scope, you won't see the nice, clean voltage ramp that the device requires, but instead you'll be seeing spikes and noise that will stop the closed loop feedback circuit from working properly. The more current flowing in the main loop, the worse those spikes will be, and the worse the error.
There's nothing for it but to improve the layout: very short wires, solid ground plane, all the usual advice applies. Ditch the breadboard, though.