Never heard of an oxidized relay, but regardless, you're looking for something that is intermittent and consistent. Pitted or arced relay contacts would cause problems either all the time or at unpredictable times.
The most common suspects are the crankshaft position sensor and the camshaft position sensor. Those often fail by becoming heat-sensitive, then they work again after they cool down for about an hour. While driving, the natural air flow through the engine compartment keeps the sensors cool. When a hot engine is stopped, the heat migrates up to the sensors during "hot soak" and that's when one can fail. This is actually pretty common on any brand of car.
The problem here is you are going about finding this the wrong way. If one of those sensors fails while driving, there is usually enough time for a diagnostic fault code to set while the stalled engine is coasting to a stop. The code may not set simply from cranking the engine. Regardless, you erased any fault codes by disconnecting the battery. Doing that is the last thing you want to do because you will lose that valuable information.
You also need to check for spark while the no-start condition is occurring. Loss of spark, injector pulses, and fuel pump are all indications of a failed sensor.
Monday, June 20th, 2016 AT 7:38 PM