Corolla / Matrix 2009-13 :: 2010 Toyota - Engine Cuts Out At High Altitude

I drive a 2010 Toyota Corolla, 1.8L vehicle. We recently went on vacation to Colorado and somewhere around Fairplay, CO, which is about 9500 feet above sea level, our relatively new car with only about 47K just died in the middle of the road where there was not shoulder or cell phone service. I pulled over the best I could and popped the hood after several attempts to restart to no avail. I removed the decorative plastic engine cover and looked at it long enough to realize I did not know anything to do or try, reinstalled the cover and closed the hood. I was then able to restart the car and go a little further.

It did happen to us one more time and again after a few minutes on the side of the road with the hood open I was able to start it. I was very surprised that there was no check engine light when I was able to restart the car. I would expect if the engine just dies in the middle of driving that it would at least produce a code where I could have some idea of what was going on. I have read about vapor lock, but it sounds like it is more likely to happen on older cars with a carburetor and with the fuel pump under the hood instead of in the fuel tank. Should I try higher octane fuel?