K1200LT Shuts Down mystery

Hey guys,

I have a 2000 K1200LT with 23k on the clock. Last week I was traveling to the NJ shore, and the weather was hot. Bike was not overheating, and the temperature gauge was exactly in the middle. I had a little more than a quarter tank of gas, and I had no issue traveling at a highway speed of 65 mph. The engine was sounding great, and I have had no mechanical issues, other than replacing the fuel pump, with the bike since I bought it at 14K. At the bottom of the exit ramp, the bike shuts off and I was able to roll to a safe spot on the side of the road. At first I thought, somehow, the gas gauge was wrong, which has never been a problem, so I put in another gallon of gas. The bike would start but only for about 5 seconds and then shut down again. I was able to park it at a local Public Storage and came back the next week to have it towed to my mechanic. Of course, the bike started right up and stayed running. It has been at my mechanic's shop for the last week, and he also can't get it to repeat the problem despite running it for hours. This feels like an electrical/digital issue and not a mechanical problem. Could it be the water pump wasn't keeping up with the temperature of the engine and a sensor shut the bike down? Does anybody have any clues of what I was experiencing that we might track down to figure this out?

Thanks for any help.