Excalibur engine hesitation

Hi, I am having an issue with my new to me 2000 Ski Nautique, Excalibur Engine with zero off.  When I first  take the boat out and give it throttle it accelerates just fine.  I shut it down while getting ready to ski, start it up, attempt to pull the skier it accelerates then shuts down as if I pulled back on the throttle(engine continues to run), I swing around to pick up the skier, give it throttle and it accelerates like it should and will be fine until I stop and shut it down then the same thing happens.  It starts right up with the push of the start button with no problem.  I thought maybe the Zero off might be causing the issue but with Zero off turned off same thing happens.  The PO said he ran hi test gas so I used the hi test as well.  It doesn't seem to matter whether I ease the throttle down or give it full throttle.  It happens whether I am pulling a skier or not.

Thanks Keno.  I will get more info