Vessel shutting down engines

You have to have the CAT tech look at the throttle signal codes.

I'm guessing your issue is related to the sea fire shut down box, or a control issue. I had this issue and it was the sea fire shut down box and we confirmed it by looking at the throttle signal or throttle position display on the CAT laptop.

The more I think about it. The less I think it's the fire system auto shutdown as that generally will shut everything off all at once.

I'm guessing it's leaning towards either the boats wiring for the ignition switches, which won't throw any computer codes. Or, it could be the engine controls. But, I'd lean more towards ignition wiring or switches.

First a faulty throttle signal should not shut down the engine. loss of throttle input should default to idle RPM. A throttle code should be logged by the ECM's. With that said if the vessel is running at cruise and one engine defaults to idle it is possible the load will stall the engine.
Now there are a few ways to shut the engine using what the ECM will consider normal and not store any codes. Key switch off, remote stop request and emergency stop request. (note some ecm's will store emergency stop request as unexpected engine shut down)
Other things that will shut the engine off are loss of power or grounds( loss of power or ground should store a intermittent voltage code), fire system protection, loose connections at ECM, customer connector, battery terminals, starter terminals, power supply terminals.
some commonly found issues are as stated the fire protection system, loose wires at the emergency stop button on the engine, azimuth tends to use the red and green start and stop buttons which are not very water protected the stop button may be sending a stop request to the engine.
Are there any other electrical items shutting off at this time?
Do the gauges continue to display accurate engine information during the shut down?
Your initial post seems to indicate that both engines are doing this, if so start with common connection points of both engines for your checks.
Intermittent electrical issues are difficult to troubleshoot.
At the dock with engine running try wiggling the harnesses to cause the engine to shut down.

Lots of good advice in this thread and wish I would have seen a thread like this back in the spring when my C18's were doing the same thing. It ended up being a ground wire at the engine. As mentioned, start the engines at the ignition on the engine itself. If all is good, then it is one of the above possibilities in CatTech's post causing the shutdown.

What engine and throttle controls do you have. I finally straightened out a Teleflex/Mores KE-6 electronic control issue that similarly drove me crazy.

The few and proud.
Bless you and good luck.

Are you saying a windmilling propeller increases the load on an idling engine to the point of an overload induced stall?

What he's trying to say, is that when the engine goes to idle from cruise speed while the vessel and other engine is at cruise speed, the drag from the propellor may stall the engine with the sudden loss of rpm's causing it to shut down. I've seen it happen if someone cuts the throttle very quickly on only on engine. Rare, but I have seen it happen.

He wrote "it is possible the load will stall the engine."

What you have described is usually an issue related to poor transient response or fuel control linkage issues on mechanical or hydraulic governors.

A windmilling prop produces negative torque ... it tends to drive the engine, not add load to it.