I would go back and verify exactly if the loosening of the oil cap is really involved. With it on and someone cranking watch the shut off lever. Remove the oil filler cap and watch it again. Any difference and you should pay some attention to this item.

I base this on the two time occurance kind of ruling out coincidence maybe. Does a loose cap blow off when just cranking? I know it does not blow off when the engine is running. You mentioned that.