what causes a weight-controlled microlight to tumble
There seem to be several mechanisms. One is an excessively sharp nose-down control input after entering or approaching a stall.
and is it possible to stop it from tumbling once it starts?
Not without an external safety device (presumably a throwable parachute or something similar)
The tumble mode is a little known mode of departure from controlled flight experienced by weightshift controlled microlight aeroplanes. It has been a very significant factor in fatal accident records, being non-recoverable without the use of external safety devices. The mode consists of a nose-down autorotation at a rate of up to 400°/s. The tumble entry mechanism is explained, and advice to operators developed which should prevent tumble entry. Evidence is shown of the nature of the developed tumble – both modelled and through wind tunnel results, which explain how the autorotation occurs. It is also shown how this theory may be applied during testing of an aircraft to develop a tumble resistant aircraft.
This seems to be an excellent
paper 255-page dissertation which contains far far far more than the average reader of this website could ever want to know about this phenomenon.
You should note that this contains stills from the Youtube video in the question. It is therefore directly relevant. If you can find a better analysis I will print out my answer and eat it.