There can be a number of things wrong like some bad connection between the coil and power source or any reason there is low power to the coil(s). The CPS also can be at fault as well as the ECM but..on any coil that has had a problem charging and discharging through the plug there is the distinct possibility of an internal fault which can be very temperature sensitive depending on where it is. I think I would start by testing the coil voltage while running on both. It should be the same as the battery but CFM's electrical components are so cheap, there usually is at least a volt drop between the source and loads. Still, should be above 13.5 volts. If below 12 and the battery is above 13.5, then there is an issue with supply somewhere. If all is low..there is something wrong with the battery or charging system. If all is OK, then I would swap coils and see if the problem now moves to the other cylinder. If so, I would consider replacing that bad coil. I would think the plug lead would come with it but who knows with these guys.