Not mine, but a friend, has a 500 Trials Replica, and has had three flat (rear) tyres in short order. The first two times, he took it in to a shop and they threw a new tube in and sent him on his way. After the third episode, he called me (not that I am a guru, or even close, but I know people), so I made a phone call to a mate and we all met up at my mates place.
Wheel out, tyre off, INSPECT tyre carcass (no objects protruding - good ), INSPECT rim (fcuk ! what a mess), most of the way around the inside of the rim, there was a jagged edge where the steel had been folded to form the bead. That jagged edge chaffed the tube, each time, and caused the puncture ! Low pressure would have helped here I'm sure.
The jagged edge was filed smooth then dressed with a wire wheel on an angle grinder, a couple of protruding spokes were also filed down, painted the whole thing (inside) and fitted a new rim tape, tube and inflated to a higher pressure than specified in the handbook, and we are good to go ! He is a big bugger, so needs more pressure than the book says - 35 psi for now.
The moral of this story - look for the cause, and not just the solution.
Aaah - Royal Enfield, making men into mechanics since 1901 !