1998 FLSTF dies randomly

[TKO]

I recently bought a very low mileage 98 Fat Boy. I've put almost 1k on it in the last 3 weeks. The bike runs perfectly... most of the time. 3 or 4 times now, it has momentarily shut off while at speed. It acts like it's out of fuel even though the tanks are full. Then, just as quickly as it die, it fires right back up and runs perfectly for another 150 to 200 miles. Twice now it has died, again, as if it had no fuel or the ignition was shut off but, on these occasions, it did instantly fire right back up. Instead it left me scratching my head on the side of the road. Both times the bike started again after 10 to 25 minutes. The new peacock, new fuel line and carburetor newly cleaned by me leads me to believe this is not a fuel issue. I  think it may be an ignition issue. This bike still has the original electronic ignition. This is the newest road bike I have ever owned and it's the only bike I've ever owned that has an electronic ignition. If it had points, I wouldn't have any questions. Unfortunately, I know absolutely nothing about electronic ignition. Could this be a bad ignition?

Any information would be greatly appreciated. 

Thanks