Executive summary: Turn off your headlight.
This afternoon I decided to take a look at this problem. My bike is an '02 640 ADV, and I have never had any trouble kick starting it. My 'drill' is: turn it on and kick it. It usually takes 1-3 kicks to start. I had a theory about what the problem was which I won't share with you because I was able to prove it wrong.
Anyway, I disconnected the battery, turned off the headlights (HIDs) and it started on the third kick. After a little experimentation, I discovered that it won't start unless I start the kick at TDC. If I take the time to find TDC, it always starts. When I kick it the taillight and instrument cluster lights come on -for about a second if it doesn't start.
So what's the problem with everyone else's bike? Incandecent headlights, that's what. I hooked up the stock H1 bulb to the low beam and turned it on. The bike wouldn't start. No way. I got a slight orange glow out of the headlight filiment, and that's it.
So, If your battery is dead enough that the bike won't kick start, just turn off the headlight -or unplug it if you don't have a switch. You may also have to disconnect the battery (just unscrew the ground lead) - I don't know if a dead battery is too much of a load.
So now that I have the gist of things, what are the specifics? I measured the current in the +12V lead of the CDI box. It draws 55mA when the motor is stalled, and 150-175mA at idle. The current goes up when the motor revs, but I don't know how far, because my meter tops out at 200mA. This is less than 1/2 Watt.
I hooked up an external power supply to the +12V lead, and found that the CDI will work with a supply voltage as low as 5.3V.
I measured the +12V when I kicked the bike over, and found that the voltage was 9.5-11.8V with the taillight and instruments as a load, and dropped to 3.5-4.5V when a headlight was added to the load.
So basically, the kickstarter has more than enough power to fire the ignition, it just can't power the headlight as well.