IL according to the wiring diagram for the Rato 670 the stator produces under 5 amps as it is fused at 5 amps. And battery is fused at 10 amps. So basically it is design mainly to recharge the battery and keep the fuel solenoid powered. Not much extra for anything else so it sounds like the OP is over taxing the system and the battery is having to provide the extra current that the alternator can't; otherwords, it cant keep up with the current draw and the battery starts draining. With the stator being fused at 5 amps I would say the stator is probably a 3 amp version.
I would be testing the amp draw to see if amp draw is too much. If it is then basically the only solution is either install a higher amp alternator, which I don't think is available for the Rato, or reduce the electrical loads.