How does it cut out, completely? or intermittent? Does it have spark when it ''cuts out''?
First thing that comes to my mind is a crack or fault in the ignition coil. Also a cut wire could do this as after a while of heating up the cut wire will separate from the power source.
Let us know anything relevant to the problem and try to describe it in as much detail as possible and we may be able to help.
Jarrah
__________________
2000 TT-R250M-
Spoiler
Ported & polished, 73mm bore, Wizeco piston, US header pipe, FMF Q4, #150 main jet, #52.5 pilot jet, throttle stop screw adjusted, larger snorkel, GYT-R air filter, NGK Iridium spark plug, 14/51 gearing, NOS +