It takes a fairly long time of sitting before a healthy, charged battery will discharge to where it won’t crank the engine - unless there is another problem.
I don’t know what exactly “AAA” applies to (other than the auto service thing). Are you talking about the person who shows up in a tow truck to help with a car problem? Or a repair shop with an “AAA” emblem or what?
In any case, many auto parts stores will check your battery and charging system for free. Have someone do this.
Your problem will basically come from one of several things:
- an older weak battery. Just because you can get it to take a full charge doesn’t mean it is fine.
- a charging system that isn’t working right (e.g. a bad alternator or related item)
- something in the car that is drawing too much power while the car is turned off.
- bad cables/connections with perhaps an interaction with any of the above.
So you need someone to look at beyond whatever the “AAA” thing was.