AS Miki stated....a leak in the fuel system that then allows air into the system.....as weird as it may sound.....try topping off the fuel tank and seeing if the ski behaves properly.
If it does, this could/might indicate that you have a crack in the fuel pickup tube inside the gas tank...there is no fuel pump in these skis. Fuel delivery is based off of engine vacuum "sucking fuel" into the carb(s). So if air gets into the fuel system, the engine sucks air and she NO GO!
Have your Aunt switch over to the REServe selector and she if that makes a difference......the fuel baffle (inside the tank) has pickup tubes molded into it on the inside of the baffle, the RES tube goes all the way to the bottom of the tank...since they are independent "tubes", if the PRIMARY fuel tube is cracked at some point and the fuel goes BELOW that point...no fuel, no go. If you switch to the RES tube and the ski responds....you might only need to replace your fuel baffle or seal the crack (with a soldering iron), if that turns out to be the issue.
On second thought, you probably can't seal the tube if it's cracked (as it is internal to the baffle), so replacing the baffle (new) or getting a good used baffle are options.