seems like I had a similar problem. The flywheel rubbed through the wires from the generator shorting out and caused just the problem you describe. Generator and flywheel had to be replaced due to arc errosion on the flywheel. The battery will carry it's charge for sometime unless of course there is interference elsewhere. Take the flywheel off (I think it need a puller) and have a look. I'll try to find some more info but probably Greasy will get in first.
Will be back soon.
Moto Guzzi V11 Rosso Corsa
Highland Outback 950
Highland Motard 950 x 3
Highland for the Body and Guzzi for the Soul