All I'd add to the above (idle speed and air filter) is the fact that the state/condition of the spark plug can have a dramatic effect on cutting out, as it does on any single cylinder motor. Do you know when it was last changed/checked? Or for that matter, when the bike was last fully serviced?

As idle speed is by far the most likely cause of your problem, check that first, then have a look at the air filter and spark plug. If one of those doesn't fix the issue then I'll eat my hat/helmet!

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