Prior symptoms which progressively worsened: at full engine operating temperature (200 degrees) the idle becomes somewhat erratic at a stoplight. When I pull away in first gear, it would "stumble" or hesitate and then take-off. This would only happen after the car had been driven for about 45 min - 1 hr. Prior to that the car would operate fine.

Today: the symptoms progressed to complete failure. After driving for about an hour, the car had a very weak idle. When I gave it gas to steady out the idle it backfired twice. It progressed with practically no engine power and then finally died in the middle of intersection (of course!). There was an immediate smell of raw gas. Now it will turn over but won't fire. The car was towed to the shop. I was afraid of an engine fire so towing seemed the most prudent thing to do.

Background: it has a Mallory electronic ignition with stock coil and correct spark plug wires, we've tested for vacuum leaks and there aren't any. The air flow meter was replaced with a rebuilt unit about 1 year ago (this could be the culprit). After the backfire it will certainly need to be replaced... again. The throttle body control valve unit was also replaced about two years ago. The cylinder head temp sensor unit is seated properly and tests OK.

Any suggestions of where to look next are greatly appreciated. Thanks.

What year, what engine? Fuel pump?

Sorry, 75' 1.8L, stock fuel injection. Could be the fuel pump. But a backfire?

If it was not for the smell of raw gas I would think it was starved for fuel; possibly dirty filter, dirty sock in tank, or plugged vent creating a vacuum in the tank. Something that gradually builds up over time.
The other possibility is some ignition component overheating causing a gradually weakening spark. These items can be checked, but you need to be prepared to do a test while the failure mode is present.

Vacuum line/intake progressively cracking until total fail!

Vacuum hoses: Hoses should be replaced every 5 years. They lose elasticity when fitted, hardening and eventually cracking. Replace the entire set with a new set.
Manifold Pressure Sensor: Cracked diaphragm, leaky case.
Injector seals: Leaks due to hardening and cracking.
Intake manifold gaskets: Cracked, poorly sealed and/or torqued.
Intake runner boots: Leaks due to hardening and cracking.
Intake manifold (plenum): Can have leaks due to seam cracks and cracks around other fittings.
Cold start valve: Leaks from the valve itself and the seal to the plenum.
Throttle body seal: Missing or cracked gasket to the plenum.
Throttle body shaft: Worn shaft leaks air past the throttle plate.
Auxiliary air regulator: Stuck open, defective valve
Deceleration valve: Stuck open, or leak in the control diaphragm
Distributor advance/retard: Either or both the advance and retard diaphragms cracked or leaky
PCV Valve: Stuck open or worn out.

Pump in front on 75 so probably not pump. 1.8 hates vacuum leaks.

Yep, even the o-ring for the oil fill cap can be suspect.

When I had my last 1.8 I took all the hoses that it didn't need that went to the elbow and machined some delrin plugs and i will do the same for my 1.7 that I will be putting L-Jet on.

For spark I used a Mallory Unilite which I'd love to have again...which due to current prices won't happen! Wow they are expensive now!