Your problem sounds to me electrical,sounds like a coil is packing up once it is hot and if it cools down it starts to work.when the bike cuts out again try removing the sparkplugs and see if you are getting a spark.check the condition of the plugs.
Also
Have you checked the fuel tap is functioning properly? This being the engine vacuum switching it on and off to let the fuel flow,i came across this on a bike years ago but the bike was running very rich the small diaphram in the tap was stuck open.(Their should be a vacuum hose connected from the air intake of the bike to the tap)
Hope this helps
Debbi
May 2008