Odd. As Jason says, this makes no sense.
To your question, at least on my US model 2.0 car, there are two charging modes, and one discharge, under "normal" conditions. The battery is charged with up to several amps whenever the car is awake, aimed at getting it to 13.77v. It's trickle charged (perhaps 100ma) when the car is asleep, again aimed at a 13.77v float charge. The source of the asleep power is an inverter internal to the ESS, and I presume the APS supplies this when awake. So bottom line, if you put a meter on the battery at pretty much any time, you should always see 13.77v. I was able to check this because I had the SC wire in a connector accessible from above when they replaced the battery back in 2015.
The only "normal" discharge occurs when the Unlock button is pressed on the key fob. It's a 20-ish amp pull on the battery for about 3 seconds. Why it occurs is still a bit of a puzzle, but it's there regardless of whether the car is locked or unlocked, and awake or asleep. If the battery isn't able to maintain at least somewhere in the 10-11v level during that time, the car issues an alert (#248).
As Jason suggested, check the connections to the battery, though after so many tries, I expect they're going to be fine. I'd also look at the 30 amp fuse under the hood. It's on the passenger side, in the corner by the windshield. While you're in there, snake a wire from above down to the battery so you can monitor it later. That might be your best way to figure out what's going on.