[ImperialCrown]

Welcome to Allpar.The fault code 12 is usually the code that many fault code reads start out with, then you get your real codes and the sequence ends with a 55. It may be normal.
If you suspect that you are losing battery memory back-up to the PCM, see if your scan tool shows 'starts since set'. A 0 starts since set would confirm that the battery supply to the PCM is being truly interrupted.
Which engine? It sounds like a possible rich or lean die at idle. Make sure that the throttle body blade and bore are clean and free of carbon. Do not adjust the minimum air screw, the PCM controls idle speed. The AIS (and other components) can act up and not set a fault code. It is always nice and easy when they do.
Fuel pressure regulator vacuum diaphragms can rupture and raw fuel will then be sucked into the intake manifold through the vacuum hose and cause a rich condition. If you pull the vacuum hose and the inside is wet with gas, this is a leaking regulator. Replace it. This is one of those 'invisible' fuel leaks.

 

[ImperialCrown]

If the idle improves by pulling off a vacuum hose (i.e.-PCV hose), that could confirm a rich condition. Fuel pressure OK?
How do the spark plug tips look? Black would be rich. Many times they will tell a story. Having to hold down the gas pedal to start sounds rich.
An ignition problem would be likely evident whatever the engine speed. Is this worse warm or cold?
Any reaction by wiggling wires harnesses?