2011 Prius infotainment/radio memory loss

First thing I noticed was that I'd shut off the car and sometimes it'd turn back on in accessory mode about five seconds later. Happens most times I shut down the car.

Later I found that the fob wouldn't work. Though the battery was low but now I suspect the car is not powering the system that "listens" for the signals sent by the fob after 8+ hours. (I end up using the physical key to get in and putting the fob next to the start button like I would with dead fob battery). When the car has been running at any time during, say, the last five or ten minutes, the fob seems to work fully as designed.

Later I find that upon each startup (at least, if the car has sat for 8+ hours) the infotainment thing does a "loading, please don't turn off" screen for 1 or 2 minutes and I can't use the back up camera before it loads. Happening consistently now under the aforementioned circumstances.

The dashboard clock, too, does not keep time of the car is left off for a long interval either.

Are my 12v battery terminals connected wrong, did something else go wrong?... I'm a bit confused. No difficulty getting the car itself to start and drive! I replaced the 12v battery myself when it started to go bad a year ago.
This is a higher mileage (a little under 200k) 2011 Prius Three

 

20min commute each morning and evening

 

What I'm seeing makes me think this is something other than a bad 12v battery. I turned the car off waiting for someone and then tried to turn it on again ~ 10 minutes later and it looked like it was trying to start, made a little click sound, but then went "dead". Now the trip odometers, A and B, are also re-set! When I shut down the car at home 30 minutes later, the power locks were no responsive for a minute or so after shutting down but then came back on