What stops the speed from just increasing.
Simply the mechanical drag rapidely equilibrates the tiny motive power...
a larger or hotter flame would increase the speed, but could be harmful for the engine !
the flame is just a source of very hot air, but not mandatory, one of my engine runs well with an hot air gun.
They will and do run for hours at a time, in fact it’s usually the noise of them that you get irritated by!
flame lickers are surprisingly noisy, and this is certainly not related to their power, nothing to compare with a Stirling engine.
it is not easy to work out the source of the noise, the flow of air through the small passages and the valve movements at exhaust. maybe a sign that some power is lost with this noise !