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It could be any number of things ... when it does this is when you need to start troubleshooting , as it could be the Coil or Stator heating up and failing , so you end up losing spark , then when it cools it will work , so you need to test when the condition is occurring to confirm or eliminate that as a cause ....
It could be a lean fuel condition , the hotter the bike gets the leaner it gets .....
It could be valves , once they start closing up , the bike may start up , but while you are riding it won't have enough compression once the engine heats up to keep compression up enough for fuel to combust
You need to check the carb , for the float level or the float sticking , as well as the inline fuel valve , if the fuel valve is bad , gas may be slowly draining into the carb , but once you ride it , it needs more fuel and the gas that has slowly drained into the bowl while sitting , gets used up , and it runs out of gas , while sitting for the 10 minutes while you are kicking it , which is what it may take for the bowl to fill enough for the jets and the accelerator pump to pick up the fuel again , then it finally starts , then once you ride again , you deplete the bowl contents and it happens again
Another electrical issue may be the CDI/ECM/ECU , it sometimes will fail when it gets warm , they work fine while cold or in colder temps , but as the weather warms , or the electrical draw warms them up , they shut down , I have seen this happen a lot in ATV's and bikes as well ...
So there is a list of things you can troubleshoot
What you did not mention is what you had already tested , if anything , and if it was tested , how it was tested , that would help with knowing what you have eliminated , or what it could be narrowed down to be ...