infinity g20 battery sporadically discharges

check if the light is staying on it the trunk. Also ensure trunk and all doors are closed properly. you could try removing fuses for the stereo and trunk light while parked overnight and see if this cures it.

If it always takes that long to run the battery down, have the generator load tested with a tester that shows "ripple". If ripple is high and the most output you can get is exactly one third of its rated capacity, there is a defective diode. With one third of normal capacity, that is barely enough to run the fuel pump, ignition system, all of the computer, lights, and other accessories with nothing left over to recharge the battery.

You can also measure the battery voltage while the engine is running. It must be between 13.75 and 14.75 volts. If it is slightly high, the voltage regulator is responding to the drops from the missing phase caused by the bad diode. As you load the system down by turning on the heater fan, head lights, wipers, etc, you'll see the voltage drop to less than 13.0 volts if there's a bad diode.