Ignition power?
There isn't a manual in our library yet on your model. Don't know if it's because there aren't that many requests for a ski as old as your's or if it just hasn't made it to the manuals section upload yet.
I've seen this type of problelm, several times, but not in a ski. I think it's in what ever type switch you have that turns on the electrical power to the ski. When you use the starter, the power is being supplied to the ignition system for a start. With the key (lanyard or whatever else is used to turn on ignition) in place, after the starter has ignited the engine and you release the start button, the ignition has the power supply to keep the engine runnig. If the ignition doesn't have the power, after a start, you let go of the start switch, then it will die.
I don't think this is the mpem. I think it's going to be related to your solenoid or your ignition switch.
Does this ski have the DESS....if so, do you get two short beeps when you place the cap on? Have you jumpered anything on the ignition system? Do you have the standard lanyard safety stop switch (which primarily grounds the engine to the block to interrupt power)? If you have a stop switch, then this could be defective. Remember, as long as you supply the starter with power, your also giving it to the ignition. You have to find out from the above statements, which one of these type kill switches you have.
Write back, paint me a better picture of your kill switch system and your lanyard.