I did some sums
A lead-acid cell is 2.1V so a "12-volt battery" is 12.6V when new and fully charged. If it drops to below 11V in use it is pretty much shot. Unless the cells have dried out - check that first of all.
Even a kick-start only needs to be able to run the lights and ancillaries off the battery at times, so add all the watts up and divide by 12, this is the current the battery needs to cope with. If it cannot cope with that current its volts drop (it's Ohm's Law), possibly to a level where the lights go dim and bike dies on you.
Example, if total power is 120 watts then you need to provide 10 amps. If the battery can only provide 5 amps then to satisfy Ohm's Law it will drop its volts until it can push some current through the resistance. The resistance is 120/100=1.2ohm Ohm's Law says E=IxR so you get 5x1.2 = 6V out of the battery and electronic ignition is certainly not going to like that.
True you have an alternator providing the power but the battery also acts as a voltage regulator, it will pull the system voltage down if it cannot cope, and if it is shot it can't cope.
Did I read somewhere that this bike has a 120W alternator, total load from lights and ancillaries is typically 120Watts so there is little left over to charge the battery. And if the battery is shot it will pull the volts down across the board. 9V is well shot. If you use a small battery and only ride in daylight all well and good but if you ride at night with an inadequate battery you may resurrect the prince of darkness.
