I'll bet when it dies the bike is hot and the outside air temp is hot??? Main fuse is cracked. This is a very well known and common HD problem. The main breaker gets a slight crack in the seam. When the heat gets to it the plastic housing expands and breaks contact, bike dies. You turn it off and back on and it fires right up. Often times you can simply pull in the clutch and hit the starter and she'll refire. Have it looked at.