Sounds like faulty BMW engineering to me. They F650 electrics are designed to work flawlessly in your garage. By design, they only fail at a fuel stop, at night, in a driving rainstorm.
I assume you've checked the battery connections? They're clean and tight? Kill switch on? Try jiggling the switch and turning it back and forth a few times. Try wiggling the wires going into the back of the switch. My 01 had bad contacts in the switch after a buncha miles, and would only work if the switch were juuuuust so in the righ spot.
"I tried to move my mind there and nowhere else and imagine a single detail that, if I didn't see it that weekend, I never would... The world is easily lost."