I have this same problem. I believe that is why I wasted money on a new battery.
What I have found is that sometimes my car will not even start after sitting. When that happens, I take the key out of the ignition, unlock the doors with the fob, push lock twice (hear the beep), and then the car will start.
If everything shuts down as you mentioned, I can pull over, stop, and do the same routine - then the car will start and all systems will be go.
I am curious to learn if your problem has been cured completely?
Thanks. CB