Driving and all of a sudden the bike has an ah ha moment! Just taking in a breath of air?

I just bought a Harley 2006 softail deluxe. When I am riding it will sometimes just die. I have to pull over and turn off the bike and turn it back on. Then it starts just fine. I have taken it to several different bike dealers and they can't seem to duplicate the problem.

It happens everytime I ride at least twice.
I am very frustrated and just wonder if anyone else has ever had this problem. Maybe it is in the security key fob electrical system? This is activated through your turn signals so when the bike is hummin' along I don't want to chance it and turn the signals on. Please help because it is getting dangerous and I can't ride on the freeway with this problem.

Thanks