The above is an excellent suggestion. Your ignition switch might be a problem, but it might not be your *only* problem.
Losing ALL your power, not just ignition via the ignition switch or power to the coil, sounds like you have a break inside a major covered wire. What I mean is, you might have a break or rot on the primary cable from the battery to a primary junction point either on the negative or positive side, or a problem with a junction block. When cold, it makes contact, but when hot it expands and with a bump or a braking/acceleration 'lean' it comes apart enough to open the circuit. A few minutes off and cooling, or just not moving and it comes together enough to work. This can happen over time in certain cases. If it was an ignition switch problem or ignition coil solely, you wouldn't be losing your lights as well. I have a Peugeot turbodiesel, and those cars are infamous for just about every electrical gremlin going due to several different causes. 1) poor and weak ignition switch--repair is using a separate HD relay to power the starter, and KF people do know that their starter buttons wear out. But that is slow or no starting rather than your problem 2) bad connections from wires to printed circuit boards that control rear lights and gauges and clock--not applicable to KF. This is the sort of problem people with fibreglass cars/dashboards have getting no power/weird stuff happening with poor grounds, especially in the Studebaker Avantis and Hawks (dash is fibreglass).
However, most important AND applicable to KF cars 3) wires, especially in the starter, charging, and primary power cables that "appear" to be just about perfect but are broken and rusted/rotten underneath the intact covering. If there is impedance, then the wire might be acting like a thermostat under load. I have had a problem with the high-beams (ie, when all four headlights are on) in my 63 Studebaker Wagonaire due to bad wiring overloading the headlight circuit and intermittently blowing the circuit breaker due to hidden corrosion that was NOT fixed by cleaning up the grounds and contacts with sanding and dielectric paste, NOR by replacing the floor switch which is also a common weak point.
I would think that a partially defective cable would like be showing higher impedance than expected, because if it is breaking, there might be rust/green rot/spark gap damage underneath. I would start by cleaning and redoing the contacts at all major points, and also by temporarily replacing the negative cable on a positive ground car. Work from there.
