I have a 2001 Sonic prowler with a 496 HO 500 hours that has developed a stalling issue. When the engine is cold it idles fine and only has an issue when I've been out running the lake for 15-20 minutes and then power down to idle. Once I power down it will idle fine for 3-4 minutes and then just shut off. It doesn't gurgle or skip or spit and sputter, just shuts off and will fire right back up on the first attempt. Out on open water it runs great, we ran it at WOT the other day and it ran fine and this time when we pulled back to the slip it did not stall. Waited 3 hours and went out again for 15 minutes, powered down into a bay and it stalled after idling for 4-5 minutes and this time would not start. Sat there for 15 minutes and then she fired, ran rough so i gave some more throttle (1500rpm) to get out to open water and ran fine once opened up. Temp is at 165, scan tool shows no codes, no alarms (may have been disconnected by prior owner, how do I check this??). New fuel filter, new gas, ran a can of seafoam through it and still acting up. Any ideas out there?

I would start by cleaning the IAC and then check fuel pressure (42 - 44 psi). Pull a few plugs to see what they may tell

Check the negative connection on the back of the engine. If that's corroded or loose it can do this.

Start with replacing the IAC valve. Motorcraft CX1766.