Jim,
I have a Beta Rev 50 2002 for my son and this does the same thing in that it revs like hell then eventually dies - most of the time anyway.
I have had trouble when power washing the thing off and getting water into the filter and carb due to the fact of a pathetic air intake box having 2 dirty great breather holes in it, so this may be worth checking but I would think this was the first thing you looked at if your model is the same.
I have tried most things to get a decent steady tickover including a topend decoke, cleaning carb and tank out etc but it hasn't happened.