To have a constant output it would mean that as the voltage decrease the current increase. But if the controller allows for maximum current with a full battery it's not possible. And it's more the opposite, you need a "high" voltage to generate the maximum current so I think everything decreases...
At one moment if you reach the maximum allowed current you can't do anything. A discharged battery will have less voltage and with the same (maximum) current the power output will be less.