Doesn't completely rule out the battery but its starting to point in other directions; Reg/Rec, Stator. Before my money left my hand I would get a test done. Google tests, plenty of advice there. I would test the Stator output Volts about 50v at 4/5000 RPM. Mike.
I've bumped mine when the old battery was on its way out, once was outside Zipsters house leaving the lights on as we chatted. Bought a SPS lithium Ion and that did go down once also leaving the lights on !! Got to return the battery to see if it's a bad one they said, will have to do it after my Mugello trip now.