2005 Prius - 12V battery keeps dying despite repairs/replacements

This has been a long road since it started in October, so I'll try to summarize.
I've had to go to 3 dealership shops through this. I'll number my regular place as #1.

October:
Event:
Gas engine cuts out on the freeway. Master light and check engine light turn on. I try to make it to the next exit but run out of hybrid battery power after a minute and have to pull over. While waiting for a tow, the 12V battery is drained. No codes in the computer.
Repairs:
Dealership shop #2 says it's the 12V battery and the computer needs to be reflashed/updated.

January:
Event:
Same problems occur.
Repairs:
Dealership shop #3 tries to diagnose, can't find anything. They run a warranty on the 12V and replace it.

February:
Pre-event:
I go in for regular maintenance at my usual place, dealership shop #1. They can't find anything wrong and replace a headlight that has been out since August.
Event:
Gas engine cuts out on the freeway, but this time I pull over right away. I call dealership shop #1 and they tell me to try to restart. I manage to restart the engine and get back to dealership shop #1.
Repairs:
The inverter water pump failed, and was replaced.

June:
Pre-event:
I've only driven every 2 weeks for a half-hour at a time since mid-March because of COVID-19. I've had to work from home most days, and only get to go in when it's absolutely necessary.
Event:
On my way to work, the gas engine cuts out again. Master light on, check engine light on. This time, I'm able to restart the engine by using a jumper pack I got, but the same failure happened twice as I limped back home.

I'm going to go in tomorrow to get yet another diagnosis/repair. I'm afraid it might be the DC-to-DC converter, which as I understand it is costly to replace. I've already had to replace the hybrid battery in 2018, the last time I posted here.

When I checked the voltage of the 12V using the maintenance mode on the MFD, it read:
11.3 V (headlights on)
11.8 V (headlights off)
14+ V (upon jumping the engine, then the MFD exited maintenance mode)

I have a multimeter in the garage and will go read the voltages from the engine compartment and from the battery connection points later on today.

Any insight on what the hell is going on would be much appreciated. If this requires a costly repair or a new car, I guess I can go back to living off rice and beans again.

Thanks in advance

 

I've got about 97k miles on the car and have regular maintenance.

I grabbed my multimeter and got these readings:
Front measurement point: 11.9V idling, 14.4V running.
Back measurement (on the battery itself): 11.9 idling, 14.0V running.

 

I've got the SKS feature and I know that's nibbling away at the 12V charge over time. I guess I'll need to do a weekly drive now if it's parasitic loads draining the battery.

 

The shop cited a technical bulletin that prescribed updating/reprogramming the ECU. The bulletin number cited was EG047-04

They pulled these codes off the car:
P3190
P0A0F

I'll go look up these codes and update the thread. If anyone else recognizes these I'd appreciate your input. Thank you for your support!

Edit:
There was a similar thread here that covers the codes:
Prius died randomly today, TSB EG047? | PriusChat

Quoting from one of the replies:
"
P3190 = Poor Engine Power. Engine has started but torque output is below 20% of expected torque. Reported by engine ECM.

P0A0F = Engine Failed To Start. Reported by HV ECU - this may be associated with the P3190 code.

My understanding is that the update described in EG047-04 TSB simply extends the amount of time before the ECM will decide that the engine hasn't caught - it'll crank a bit longer. That doesn't sound like your problem.

The P3190 code is likely the root cause of your problems, and the recommended course of action is:

- Check the air induction system (intake) for leakages or blockages
- Check for unusual noises or vibration
- Check the fuel pressure
- Inspect mass air flow meter
- Inspect engine coolant temperature sensor
- Inspect crankshaft and camshaft position sensors
- Inspect throttle control motor and position sensor
- Replace the ECM
"

Other posts I've read so far have cited things like the throttle body needing cleaning. I'll call the shop back and ask if they inspected these issues as well.

 

Unknown, regarding what they actually did in October. I'm convinced that dealership shop just wanted to me off - I've since learned that the 12V battery I had then was still under warranty, but they charged me full price and even more for the "reflash".

I called my regular place. They explained that, for now, the ECU update should be sufficient.
If the low gas engine power was due to the other possible causes (blocked air intake, air mass flow sensor issue, or dirty throttle valve) there would be other codes present to indicate those. If the car stalls out again, then they'll do more diagnostic tests to check for the other possibilities.