I am very grateful for all your help, and therefore I felt obliged to write one last post to inform you about how this problem has ended.
After the lasts tests with the mechanical regulator pointed that the charging system was working well, I decided to replace the original regulator with the mechanical one. Took the bike to work today, with the headlight on all the time. It started with the starter motor every time, and when I arrived, the battery was loaded as to crank the engine again.
So it seems that the electronic regulator goes south gradually and it is unable to regulate the alternator output to provide enough power. Something like what happened with the mass air flow sensor of my car: it degrades gradually that you don't notice the lack of power until it is too late.
I have no qualms using a mechanical regulator, so I just installed it where the old one was.
Thanks again everybody for taking the time to reply and give a hand, and also thanks to all of you who read the whole thread through even when you have never heard about this bikes. I just hope this thread has been informative.
