Hi,
Stator could be breaking down with increase in engine temperature. I also have a 2002 Beta Rev 3 250 and my stator problem caused the bike to cut out after about 3/4 of an hour running. It would restart after cooling down. I had it rewound but then it wouldn't rev (problem with high speed trigger) so I bought a new one from Lampkins.
I am very interested in you're problem as mine runs poorely under load. It sounds like it's 4 stroking or pinking and doesn't pull cleanly. I've tried everything and would now like to find someone with a similiar bike to swap things over. I've replaced the stator, coil, HT lead, plug, rebuilt the carb, flywheel, new main bearings, and a new piston. I've tried replacement CDI, stator, and coil just incase one of the new items was faulty. I live in Northamptonshire, Nr Banbury. Anyone got any ideas?