P1684 is Battery Disconnected within the last 50 starts. P1391 is Intermittent Loss of CMP or CKP (Loss of Cam and/or Crank Position Sensor(s))
Other codes are present, and at least one of them the problems are known and due to be repaired as well. The two other codes are P0123 and P0456.
Fully story: The car starts and runs fine until it gets hot. Once it's gotten hot and been driven for a while, it starts acting like it's cutting out. Not a miss, more like a temporary but complete loss of electrical to the engine. It never does this when it's cold. It even stalls when sitting at a light. Again, it does all of this only when it gets hot. It's not a coolant issue. Good coolant and a new water pump. Coolant is circulating and fans/sensors/thermostats all operate correctly (to the best of my knowledge). I understand the EGR/EVAP system can cause some funniness, but those wouldn't completely kill the battery connection to the computer.
My issue is that P1684 being combined with P1391. I suspect the PCM is faulty, as I have not removed the battery connection in any recent time. The connections are clean and intact, both on the battery, and on the PCM. Is there another subsystem that could completely disconnect the battery from the PCM without physically disconnecting the battery? Perhaps the under-the-hood power relay box?
Any ideas, tips, or other inputs would be appreciated. Thank you for your time.