My propane fireplace works well when the fan is off however when it is turned on the flame slowly jumps off the burner and then goes out. Why?

Either you have a vent obstruction or cracked heat exchanger. Is this unit just gas logs in a woodburning fireplace or a unit designed for use with propane? Make and model number may help.

I'm guessing bad heat exchanger, it is a very dangerous situation and it's time to call a pro.