The oil injection system is very reliable, but like anything else it does require some basic maintenance, the oil filter needs to be replaced, I do mine every other year, and the oil injection lines can become old and brittle. And yes you should have an alarm when the oil tank becomes low, the oil tank holds over one gallon of oil, my alarm comes on with about 1/2 tank of oil left, so you should have ample warning. Lack of oil can be a possibility of engine failure, but that's usually not the case.
Also make sure you are using the correct oil, you should be using either a mineral or synthetic blend API-TC rated oil. Use of a TC-W3 oil is not instant death to an engine, but it certainly will shorten engine life.
A more likely cause is a lean condition caused by faulty fuel lines, if your ski still has grey tempo fuel lines this is a real possibility. Modern fuels with ethanol tend to break down the glue binder in these fuel lines and a green goo will be distributed through the fuel system causing a lean condition.
All that being said be certain that your motor is seized. Like ragtop said remove the pump and make sure it's not the pump that's seized, it also could be a jammed starter bendix.
Lou