'87 Century 3.8L Stalling Problem

I bought a used 87 Century 3.8 a couple of weeks ago, and I haven't been able to pinpoint the exact problem yet. When driving on a freeway or other street with no stops, it runs great. After it has been running for half an hour or so, it stalls out when I come to a stop. It starts back up immediately, but won't stay running for long. If the car sits for half an hour or so, I can get another few minutes out of it before it begins to stall again.

When I bought the car, the previous owner had replaced the Coil Pack where the spark plugs plug in, and the crankshaft gear sensor. When I bought it, it seemed to be having air flow problems. I replaced the Oxygen Sensor, which was I noticed was physically broken when I removed it (the ceramic sheath was cracked). I also replaced several vacuum hoses, mostly going to the main vacuum tank underneath the car, and a couple that went to the Cruise Control. I have also replaced the Idle Air Control, the Throttle Position Sensor, the Fuel Filter, and the Mass Air Flow sensor, as well as the air filter.

I have the unit that plugs in under teh dash to generate codes. When I replaced the O2 Sensor, it stopped giving errors for that. It was generating errors for the TPS, which I hadn't calibrated to the exact right voltage. I seem to have it now. Now, it is generating an error saying the Exhaust Gas Recirculator (EGR) is giving a problem, but I don't see any problems with it.

I have done several searches across the Internet for similar problems, and noticed that there are several people who have Century's within a year or 2 of mine who are experiencing almost the exact same thing. If anyone has any idea of what could be causing the problem, it will most certainly save me a broken hand after punching this car. I appreciate any help anyone can offer.

A lot of things are going thru my mind as to the causes, however it is hard to pinpoint the problem as some parts have already been replaced.
It is possible you may have a weak fuel pump. When the car stall, the pressure should be holding at 40psi. If not, bad pump. Another thing is you may have a bad crank sensor. When the car stalls, pour cold water on the crank sensor to cool it down. If the car runs again for a while, replace it. I'd get the car scanned for codes and other sensor parameters. TPS should be around .40v otherwise it will affect the running of the vehicle. Even the EGR could be a problem. It may look good, but does it hold vacuum when applied to it? That is one more test you can perform on the EGR.
Good Luck.

Food for thought; many of the GM front wheel drive vehicles had problems with the torque convertors not disengaging at idle resulting in a situation similar to not declutching a manual at a stop. You might try disconnecting the connector to the clutch and driving it a short distance, trying to duplicate the stall. Bear in mind that much of the 4th gear fluid flow runs through this clutch. Make this a short trip. Ray

We had similiar problems and replaced so many parts that we were driving ourselves crazy. We finally had to replace one of the injectors. But before we replaced:
oxygen sensor
crankshaft sensor
computer
Mass flow
fuel pump
plugs and wires
control module