We do get cold here but, in the course of a year, it's a small amount of time. I'm going to check into the starter maintenance mentioned here, along with some other TLC items. Happy to do anything that helps things and doesn't cost anything but time and elbow grease.
I think that I mentioned before, the bike overall seems to be in good shape. Hopefully that is not just my BMW ignorance. But it was complete, clean, and running decently when I bought it. The charging thing is just the very first problem that I had (and right away) and, upon doing a little net searching, I found that it is a common issue with these. So that's why I thought that would be the first thing I would learn about and maybe try to improve, or at least remedy.
I was out of the country for about 6 weeks shortly after I took possession and came back to cold and rain here so that is one reason that I have not been able to do much with it - either riding or wrenching. If we can get just a bit warmer (rain seems to have stopped for now) then I can get back into this. Riding to see what I'm up against and then deciding what to do if I am still having a problem. Hopefully I'll get lucky and the new battery and some connection cleaning will take care of things.
Thanks for the tips.