This one happened to me this morning. Went back in the house to get something, came back out, no key recognized. I had to go back in and get my FOB. My phone never left the car, just me. Of course, my kids opened and closed their doors 738 times in the 30 seconds I was inside, so that could have contributed...My scenario is the first one you described. Car on, exit when phone is in car, return to car but PaaK not recognized.