It sounds like the carburettor bowl is draining within the course of a minute or so, and it is not replenishing itself sufficiently quickly enough to keep running.
You'll need to remove the carburettor bowl and float mechanism, and give it all a nice clean up, wiping out any gunge, and more importantly, use a sewing needle to ensure the tiny jets are not clogged. Re-assemble and advertise on e-bay as not working!! (Only kidding! this should fix it)
Tim, June 2007