Attenuating op-amp circuit with offset
The LM324/LM358 can only sink a few tens of uA down to (near) the negative rail. Try increasing your resistors and maybe add a pull-down resistor. From the datasheet: 

 

Note that the 50uA is nominal, only 12uA is guaranteed, and that only at 25°C. 

I would suspect your SPICE model is not very accurate if the simulation does not reflect actual behavior better than that.