Most likely a bad connection to the Rectifier/Regulator or a bad Rectifier/Regulator itself. First carefully check all connections to the Rec/Reg. Pull the connector and look for a broken or corroded pin. Tug on the individual wires going into the connectors to be sure none are loose. Look at the fuses to be sure they look OK. Check battery connections and be sure they are corrosion free and very tight (wrench not screwdriver). Without a test harness it is difficult to test the Rec/Reg. Normal output voltage is 15 volts. You can get an idea, by testing the voltage at the battery with the ski running............it should be around 13V or more, but this is not absolute if the Rec/Reg is working OK. Most good batteries will have a voltage of around 12.6, and this is what you should see with the engine off (you need an accurate multimeter).
If all the connections look good, I'd look at swapping out the Rec/Reg with a good one. Stator problem is much more rare, and also much more difficult and expensive to repair.
Rec/Reg is #22 in this diagram: