The main battery cable goes to the solenoid, so it is always "hot". In normal operation the make-n-break arcing generates a black/gray powdery residue, that after hundreds of start-ups can generate a conductive path to ground. There could also be a medium or high resistance leak to ground in your key start switch. I've seen just that in old high mileage motorcycles where the ignition switch's internal metal/copper/brass electrical contact parts wear over time, transforming the factory lubrication grease into a mildly conductive paste. It slowly bleeds a small amount of power to ground, that over a few hours/days time, KILLS the battery.
Your Ohmmeter will reveal if there is such an anomaly by testing each of the disconnected wire terminal's resistance to ground. A quick check is to put your multimeter in the 10 Amp mode, disconnect one battery cable and place the meter leads in series with the battery terminal and the disconnected cable terminal. If there's no reading on the 10 Amp scale, drop down to the 200 ma range. It should read no more than low single digits. Check the blocking diode in the charge circuit too. The diode's pass and block resistance values and charge coil resistance values are listed in the service manual.
2009 EF1000iS, 2011 EF2000iS, 1987 Honda EM-3500. (ready for anything!)