Warren,
Sounds as if you have an almost perfect day ahead. Enjoy the car show.
Do you lose the high beams when driving only or will they cut off if you turn them on and just let the car sit for a while. If it is only when driving, you could have some loose connector that the vibration is causing to lose contact. I am guessing that you have checked the relays and they are actually releasing instead of staying operated when you lose the high beams. It won't hurt anything to do this, so try wiring across the relay and turning the high beams on and see if they stay on. That will either eliminate the relay or point to another problem. If the relay is releasing after a few minutes, then you have to be losing either the voltage through the winding or the ground to it. By using a clip cord and jumping across the contacts, that will tell you if the problem is in the relay area or not. I have used this method and only once did I find the relay to be at fault.
Ron