Suddenly shutting off simultaneously both engines DDEC III 16v92

I'm 99% sure it's your seafire or halon fire system shut down. Check the pressure on your fire bottle, if it is low, it will trigger the engine shutdowns. It could also just be the brain box going bad, run the boat with the little switch on bypass. That is my bet, the other 1% it could be is something with the engine controls, early Sturdy units, but doubtful.

The fire bottle will still discharge if the temperature is hot enough to melt the discharge. The engines just won't shut down.

Because the relay box or brain for the fire system is bad. Shutting off the ignitions and turning them back on resets it. It's most likely is the lower box mounted engine shut downs in the picture, there is most likely a relay in there that's bad. That is why the generator isn't shutting down, it has a seperate shutdown box (top/right). Hire someone who is competent in fixing the problem.

Because the relay is BAD. It has nothing to do with your fire bottle discharges, it reacts after the bottle starts discharging and shuts the engines down, just as if you switched the keys off.

No, it's more common for a cheap electrical relay to just wear out and falsely close than for a justifiable reason (fire bottle discharge). The Relay or pressure operated switch is old and BAD/DEFECTIVE, so it is shutting the engines off for no reason at all....not because it is doing the job it's supposed to do. You need a NEW RELAY or pressure operated switch. Open that and the generator box, if they use the same brand/type of relay swap them and see if the shutdown issue moves over to the generator. I'd just replace it and keep a spare, the relays are probably cheap.

In your era of DDEC it was very common for the relay to do nothing more than send a shutdown feed/code to the DDEC computer, just as if you turned the key switch off.

An owner I worked recently flew me from Fort Lauderdale to Jacksonville and back the same day and paid me above and beyond what I charged him for this very same problem. The local CAT dealer had been out 3x and couldn't figure out the problem. I found it and fixed it in 2 hours with their help of having the laptop plugged in. It took me most of that time to find the Halon shutdown box.

NO. Each engine has it's own DDEC boxes, battery banks etc. They're alienated. The ONLY things both motors share electrically are the controls (shift throttle) and the fire shut downs that I can think of.

Yes, those are the engine controls. I think, if that fails both engines go to neutral and not shut down. You would need to call Sturdy to find out, they were the manufacturers. Check the battery bank those are powered by.

I have similar DDEC controls but not the series III. I would check the Fire suppression system first as suggested by Capt J. If that checks out fine the next thing I would look at would be your DC power supply system to the DDEC. Most of these boats came with a DC converter to supply the 12v power to the DDEC. How is yours fed the necessary DC power? Series III may have changed to 24v I'm not sure.
On my boat I have 24v starting system but the DDEC uses 12v so it originally came with Vaneer (sp?) converters that supplied 12v to the DDEC system from an AC source. Prior to me owning there must have been a problem with the Vaneers as someone pulled a 12v leg from one of the starting batteries that are in series for 24v. This caused a big uneven load on the batteries and gave me fits until I figured out what was going on. I didn't like the original set-up with the Vaneers so I installed 2(ea) dedicated 12v batteries (1 for P and one for S) and found 24v to 12v battery to battery chargers. So now my DDEC is fed from the on-engine alternators when running or from battery chargers that maintain the starting batteries. Has worked well since I installed 4 years ago.
As a side note, Capt J is correct, if the ERIM fails the controls default to neutral and idle.