The degaussing circuitry is only activated for a few seconds at turn on. And once activated, you can't reactivate for some time (components need to cool off). So, if you have the need for serious degaussing, simply leaving it on overnight won't help. You'll need to cycle it on and off many times, with long waits in the off state.
In severe cases, it's best to use a separate demagnetizer (if that's the problem with your splotchy screen).