Think that if he says "without warning", that means the machine is idleing along fine and drops dead without beforehand missing a beat. Only a spark problem can cause that. Or a Boyer that is running just at the limit of it's ability to stay alive because the battery is totally dead...mine won't start if the battery is too dead, and I mean with the kickstart, I have no starter motor.
If on the other hand, if the thing starts to slowly lose rpms, starts coughing and then gives up the ghost...that would perhaps point towards the carbs or a plugged fuel filter, or if the tank is full, full, maybe a blocked gas cap vent(vacumn in the tank).
In my limited experience, those carbs will keep the motor running even if they are in very bad tune or condition, last summer, mine started to run a bit rough in France on holiday, and 4 days and 500 miles later, I got home and finally bothered to look at the bike. Turned out one main jet, complete with the alloy holder, had fallen into the carb bowl. The bike still started up, ran pretty ok, you just needed to give more gas to get away from a standstill...so the motor can't be too fussy what it gets from the carbs...not fussy enough to cause the bike to die without warning.
He has to explain exactly what the machine is doing before anyone can send him in the correct direction.......I bet the carbs are still good enough to at least keep it running and the electrics have a loose connection somewhere...Peace!
Have you synced the carbs lately? No, that won't cure this problem but it will help to isolate things. Remember how to sync the carbs, how you keep it running on one cylinder while you adjust the air screw (with the idle turned up a little to keep her going)? Well, do that and see which cylinder has the problem or if it happens on both. You might find that one cylinder is cutting out and taking the other with it. Yo ho ho we'll all go down together type stuff, it is British afterall.
Anyhow, try that and make sure your idle speed is set per the book to begin with! Hmmmm, well maybe that carb syncing might just cure things afterall....