Roughly, it sounds like your battery is getting worn out. In my experience when batteries reach their end, that means their "capacity" gets too low. Your test there is exactly what would challenge a battery with low capacity. And it's the sort of test I would do in my driveway on a doubtful battery to confirm whether it needs replacement, regardless of what my battery testers say.
Some numbers to consider ...
That's the battery in my 2011 LX, from Home Depot. In the upper right corner is the capacity spec: RC MINS:120
That means the "Reserve Capacity" is 120 minutes, as in two hours. So if the battery is fully charged, as it would be after driving, with a 25 Amp draw, it will take 120 minutes before the battery voltage drops below 10.5 Volts, which I guess is considered the point at which the car will probably not start. <== that is what the specification is designed to mean.
You could measure your current draw in ACC mode if you've got the right tool, but I'll suggest it might be around 20 Amps. To make the math easy (Friday afternoon, you know ...) call it 25 Amps to match the spec, and say your battery has the same 120 minutes RC MINS spec as mine does. So that means it should last two hours before getting dangerously low (when the battery is new) vs. your 20 minute result.
It could be you're drawing a lot more than 25A. Or it could be that your battery is getting toward end of life. For me, low capacity is always what ends a battery for me. If all you need to do is drive, stop, turn off, turn on, start, etc. you can have pretty low capacity and it will get it done. But sitting with the engine off drawing power will cause problems quickly.