87 Lesabre stalls

I have an 87 Lesabre 3.8L that has developed an annoying habit. It runs great for days and days...then sometimes when it has been driven until it is well warmed up, then turned off and restarted it will run for 2-3 seconds then stall......it will do this as long as you want to try it......if you let it sit for several hours it will restart fine and may work fine for days until it feels like failing again.
So far I have changed the fuel filter, fuel pump and sock, and the fuel pressure regulator. The pressure stays steady at approx 30psi when the car is running. I do not know what it is when it wont start because it always seems to fail when I am at work and my wife is driving it.
There are no codes set and the SES light never has come on. The fuel pump also runs for a couple of seconds when the key is turned on, even when the car wont keep running. Cant say for sure if it runs when the car stalls, she cant hear it and I cant hear it from work :-)
Anyone ever have a similar problem or know of a check to do or maybe a fix???? I think if I take my wife's keys that will fix it but she doesn't agree :-)
Also does anyone know if the fuel pump/relay is controlled by an oil pressure switch or the ECM when the car is running??? Or is it turned off by the cam sensor or the crank sensor thru the ECM???????
Thanks.

You could try a can of carberator cleaner inside the throttle body, sometimes works wonders on those engine gremlins. Spark plugs ok??

I will have to look at my diagrams to be sure, but I thing the ECM signal goes to the relay and the oil pressure switch is in the line back to the fuel pump (in series). As far as I know pump is commanded by the ecm to run as long as the engine is running (probably monitored by the ecm checking the crank signal). The pump may stop running due to the relay or the oil switch. There is a green connector up by the battery that goes directly to the high side of the pump. It is the fuel pump test connector and is not connected to anything. When the fuel pump is receiving voltage, there is 12 v on the test connector. I have wired up a small 12 v bulb between the connector and ground and brought the bulb out near the windshield. That way I could tell if the pump was getting the signal to run when it was supposed to. 2 seconds when key first on and always when running.
I am thinking that since the ecm controls the injectors, if it thinks the engine is not turning, it will shut off the injectors and that will kill the engine faster than loosing fuel pump pressure. I am thinking even after it dies, you still have good enough fuel pressure. Has it ever died while driving?

I checked the voltage at the green connector at the battery before I changed the pump, thought maybe the voltage was low due to a corroded wire or connection. Good idea about the lightbulb.....I will go and hook one up before I go to work.....then if it dies again at least I will know if there is voltage to the pump.
It has never died when driving, only after it is warm and then immediately after it is restarted....and again only when it feels like it, which is always when my wife is alone with it....still think taking her keys would be a good cure but it is her car :-)
I was thinking the same thing about the ECM, since it dies so quick after restart i was sort of suspecting that the crank or cam sensor was shutting the engine off.......but I checked them for damage, as best as you can do with a mirror, made sure the connectors were not corroded, oil filled or damaged...then tried to start the car with either one not connected, to see if it acted the same, but of course it wouldnt even start as the ECM didnt get a signal.
I have cleaned the throttle body, tried tapping the MAF sensor to see if the engine stumbled...even removed the intake tube with the MAF sensor still attached and tried starting the car.....once again trying to duplicate the problem.......but although it did start and die apparently it isnt the same way.....may just replace the MAF sensor for the heck of it pretty soon.
My next best guess is the oil pressure switch if there is one, then the fuel pump relay, or the ECM itself..........need the thing to break when I am around.
Thanks for the suggestions. Feel free to offer more :-)

One thing that does happen when the engine goes above 400 rpm is that the spark timing is switched over to the ECM and it uses the crank, cam, TPS, and maybe other sensors. Below 400 RPM, the spark is controlled by the ICM directly, using the crank and possibly the cam sensor. Again, I will have to look at the diagrams to see if the ICM is connected to the cam sensor.
On the 87, the crank and cam sensors are fairly cheap (~$25) and are fairly easy to replace.

I was wrong -- the oil pressure switch is in parallel with the fuel pump relay. The manual says that if the relay fails, it results in long crank times because it takes a while to build up enough oil pressure to apply voltage to the pump.
Also, the cam sensor does go to the ICM (actually the CCCI or C3I, under the coils). But the manual says that if the cam sensor fails while running, the engine should continue to run, but wont restart.

Ok that makes sense...so I guess it is pretty much the same fuel delivery system as my Fiero....just add into the mix a cam sensor and some other distributorless ignition stuff :-)
So the fuel pump relay can die while the car is running as long as the oil pressure switch is good.......which isnt my case as the pump runs, the car will start but then dies....hhhmmmm
Kind of looks like it may be a dying ECM or possibly a MAF sensor or a loose wire or a sunspot or gremlin :-)
Guess I am going to have to get it to break when I am around...preferably right next to the garage :-)
Thanks for the help.