So it sounds like something is failing once it gets hot. I'd plump for an electrical issue, something going out of tolerance when hot. Possibly plug(s), more likely a coil.
I'm not sure if the stator failing (which is not uncommon) would cause the issues you have or just effect the charging system, but if it were that I suspect you'd end up with a flat battery, so its probably not that.
One other thing to check is that the tank is not air locking, i.e. the breather is blocked which slowly causes a vacuum in the tank preventing the fuel from flowing. Easy test - when the fault happens open the tank, if you get a big sigh/ intake of breath and the fault goes, a blocked breather it is.