My lc4 charges only when it is revved above idle. At idle the draw from the parking lights and whatever other reisitence there is only allows the battery to sit at about 10v as well. Test your bike again (if you have not already) at higer rpm and see if that does not help. I've also found that with the headlight on the battery will not charge even at higher revs.
I always chalked it up to a weak stator, if you find a fix please post it here, I'd love to learn what you find out.