Besides battery, check your bulbs. If you've got a big wattage auto-bulb in headlite or taillite, you could be trying to overlight wheat your system can put out.
My guess is it is the relay above the secondary clutch.They were famous for it and gave the same symtoms as you described.Usually the speedo will read something like 140 or something crazy also.You can get the relay from skidoo or go to your local auto parts dealer and get one for half the price.The Napa part number is AR-201.