328 stalls with no warnings

What makes you think it's fuel related, and not ignition?

 

Almost impossible to tell without seeing it but some ideas: it could be either fuel or electrical.

On the fuel side you'd be looking at something like the electric supply to the fuel pump, possibly relays, maybe the pump itself.

On the electrical side, a bad connection somewhere around the fuse board or in the ignition switch (does the whole car die or just the engine? ). If its the whole car you could also be looking at a battery or earth/ground problem.

On the ignition, could be a problem with the ignition box or maybe the crank sensor(s). Its unlikely to be the coil(s) because you'd just lose one & it would probably continue running on one bank, so it must be something that affects both banks together.

 

I had the same problem.
The car would stall without warning. It could sit for a few minutes and start up, or sometimes it would take 40min to an hour. Sometimes it need a boost. This went on for a couple of months.

But in my car it was a bad ECM.
My car sat for a loooooong period of time before purchase and there was a lot of corrosion within the wiring, regardless of the fact it sat displayed in a climate controlled environment. -big problem with lo mile cars

I don't know about the Bosch FI system and what it consists of, as my car doesn't have one.
But I replaced the ECM and wiring harnesses(wasn't cheap) and never had the problem again. As a matter of fact, my old, finicky, & unreliable Ferrari runs better now than any car I've ever owned!

But I would check fuel system, electrical, and ignition as Iian prescribed first, before diving into a major undertaking like this.

It could be something simple and inexpensive like a faulty sensor or some frayed wires.
The tough thing is, if you can't diagnose it yourself your at the mercy of the mechanic.
I hope you have one you can trust.
Good luck

 

Usually an "out of the blue" stall, especially if you're under throttle is electric related, not fuel. Fuel problems usually will show with popping/missing prior to stalling. (Of course, if you're running too rich, then you'll get stalling as you come down to idle as fuel pours into your cylinders.)

You'll want to check the electrical connections and distributor leads...as well as the plugs to the ignition unit.

 

Connect a voltmeter to the fuel pump so that you can see it while driving. (I know this will not be real easy). When the engine dies, look at the voltmeter and see if you have 12 volts. If you still have 12 volts, the problem is not connected to the fuel pump circuit. If you don't have 12 volts, start "backing up" in the circuit until you do see 12 volts.

You may have to try this remote voltmeter setup in several locations (i.e. coils, engine computer, etc.) to find the problem.

 

For me to finally diagnose this same issue on my mondial, I needed the right conditions. Usually mine would quit in the driveway when I was warming it up, or putting down the driveway. But it would restart immediately and I could never find the issue in spite of extensive troubleshooting. It was clearly ignition, as the shut off was instantaneous just like I had turned off the key. (As it turned out...it WAS like I had just turned off the key!)

One day it finally did it on the highway at 80 MPH. I left the car in gear so the momentum was turning the engine so I could try jiggling the key. I jiggled the ignition key and the damn thing fired right off again. (BTW, don't leave it in gear too long as the car will be injecting raw fuel into the engine with the ignition off as long as it's turning).

When I got home I pulled the ignition switch out (not too hard...you just have to find the little release pin and feed the wires up the column a bit so you can get the switch a few inches out) and sprayed some plain old electrical contact cleaner in there. Problem gone. I have experienced lots of issues with old dirty electrical contacts on my old Ferraris. Everything from window switches to ignition switches improve tremendously without 30 years of oxidation on the contacts.

Birdman