Our propane water heater works fine AS long as the outside temperature is below 78 degrees, then the pilot light goes out.

The water heater is located outside, we are able to re light it fine, but what a bother.

What could be causing this?

That's unusual, but it always comes down to how good the thermocouple is and how the flame hits the tip. It should always hit the 3/8" part of tip and no more, but it could also be failing and oversensitive. Another thing could be that the gas pressure is changing if you have LP gas. If the pressure goes up it could make the flame cover too much of the tip making it fail. Look at the flame when it's cold as opposed to when it's warm and see if it changes. If so, then all you need to do is to adjust the thermocouple back some so that only the tip is in the flame. I bet that thermocouple is on its last legs, so you probably should change it and keep old one for an emergency. They are fairly cheap.