You said if you change the plugs the problem goes away for a while, How do the plugs look that you remove? Oil fouled? wet with fuel? normal gap?
what color is the insulators?
The L.H. control monitors the operation of all the cylinders, if it detects a misfire it will turn off the injector to that cylinder(no fuel/no power)
The question about caps,rotors and wires is relevent but should also include testing the coils (2), I've also seen E.Z.L.s with weak output to one coil.
Mike