97 Sport runs awhile then dies

I’m having some trouble with my ’97 Sport Nautique. PCM GT-40 engine. I replaced the fuel filter when I got it out of storage as I usually do, and this year I gave it new plugs, wires, cap and rotor. 

First time out I noticed my fuel consumption has increased. On our 4th outing this summer, we ran the boat off and on all day. On our last run of the evening, I left the dock, gave it moderate throttle to get to about 20 miles an hour and it died. No drama, no coughing, just stopped. It would not restart. It would turn over fine, sometimes “catch” like it was starting but as soon as i released the key and the starter quit turning it would die.

I got towed to the dock where it sat until the next day, roughly 24 hours. I was going to be towed to the marina by a friend, but I tried to start it before we left, it started fine. So we made it to the marina under our own power with no problems. I took it in to the our local Nautique dealer as we were about to leave town for vacation. 4 weeks later they got to it and the first thing they found was a faulty starter, so they replaced that along with the battery cables/ends. After that they ran it and tried to diagnose it but it ran “like a top, nothing we can find wrong with it at this time.”

So this past Saturday we took it out for the day. It was a bit more difficult to start when I first put it in the water, but then it ran fine. We tubed and skied in several sessions that day, with an hour or so break between each session. with the exception of one time early in the day where it took a few turns of the key to start, it cranked fine and ran great (though still burning more fuel than last summer). Third session out, idled for a few minutes while a kid got situated on the kneeboard, and it died. No warning, just died and would not restart. We got towed to the dock where it sat for a few hours, then I tried starting again, no luck, so towed back to the marina.

The next evening, so roughly 24 hours after it died, I hooked up the water hose and it fired right up and ran smoothly.

It seems that whatever the problem is, either time or heat is causing the shut down. 

I have some videos of trying to start it right after it died, several hours later when I tried again, and a video of when it cranked right up after 24 hours. I can post these if they would be helpful.

Any suggestions would be helpful, I’m am hoping I can get it fixed myself this time and not have to wait in line another month at the dealership.