That's typical of a failing crankshaft position sensor or a camshaft position sensor. They often become heat-sensitive and fail after the heat from a hot engine migrates up to them when it is not running. When there is no fault code stored in memory, the easiest way to see which one isn't sending a signal is to connect a scanner, (not a simple code reader most auto parts stores use), to view the live sensor data. Those two sensors will be listed as "no" or "present". If either signal is missing, the Engine Computer won't turn on the automatic shutdown, (ASD) relay. That relay powers the ignition coil(s), injectors, and fuel pump.