So by my math you're filling the car around once a month?
If so, there is the possibility of the fuel separating slightly, lowering Octane.
The Evaporative Emissions could be leaking slightly, fuel is escaping.
If you're going to try and let the car warm up for better MPG, don't let the car run. Buy a engine block heater. Kw/hr if far cheaper.
Don't "think outside the box".
There is no box.