Constant current battery discharge
With 0.6V across R2, Vce on Q1 would vary from 0.9V down to 0.4V during your DC sweep. So you are operating Q1 very close to saturation and at the lower end you can't rely on its Hfe being much more than 10.

So Q1 is probably being starved of base current. You can try to improve its performance by reducing R1 to 220R.

But if you need more accuracy than that, I would suggest a rail-to-rail opamp sensing voltage across R3 (which should be somewhere around 2R to 5R) driving Q1.