Get under there and kick it. If you hear it rattle, chances are good it needs to be replaced. Especially if it'* the original Cat that came with the car.

If the catalytic convertor were locked up usually it would be evident when out on the highway. A lack of power, especially in acceleration will be noticeable as well as maybe sounds of pinging in the engine due to high combustion pressures. The best way to check the converter is with a pressure gauge put in the socket of the oxygent sensor and running the engine. The pressure will build up.
Sometimes you can tell if the converter is bad by knocking it as mentioned. Just don't do it with a hammer or it will be bad. Make sure that the rattling that you may hear is not heat shields.

On the matter of your engine running, I had the exact same problem and no codes that could tell me anything other than 58. I finally came to the point that it had to be the MAF sensor and just changed it and it was fine. If you disconnect the MAF sensor, it should run in the "Limp" mode. This mode just substitutes values in by referencing other sensors such as rpm and throttle position and comparing them to a table and then assigning a MAF value that will work (just not the best).

Now, you were saying that it would die after about ten minutes. Same problem I ran into last year when the crank sensor started going on my car. When the sensor heated up enough the output value drop down below the threshold for the zenor diodes in the control module to actuate. The car would then stall. Letting the car sit for 15-20 minutes would allow it to start again like there was nothing wrong.

Check your plugs as well. The back 2 closest to the alternator are a continuing problem with mine. They get carbon tracking on them and creates a miss (usually under load). How does the fuel filter look? If you have any question as to it just change it. It may be supplying enough fuel to the engine at idle but under heavy acceleration it may not be able to get it there quick enough and pressure may briefly drop.

Anyway, hope this is some help.

What the heck is in a catalytic converter? What'* it look like inside too? (sorry for being slightly offtopic, but i'm just trying to add to mine/everyone'* knowledge.)

Well, My valve came in and I have tried it. It does not die quite so easily but the problem is definitely still there. After it is good and warm the Idle becomes VERY rough. I can give it gas slowly and then release and it will then idle a bit smoother at about 1700 - 1800 rpms for about 1 to 2 minutes then it will drop to under 1000 and become rough again. IfIi advance the throttle too quickly it will die. I cleared all codes and no new ones have appeared. Could the crank sensor be causing this and can I change this myself without any special tool? I must sell this car or my Opel Vectra three months from now because I am buying a Van for my wife near the end of this month and because I am military, I can only own 2 vehicles while I am here in Germany. I would much rather keep the Bonneville but if I cannot fix it soon then I will have to accept my losses and it will go to the junkyard.

have you checked coils yet? the ohm of them...maybe you have a bad one...or wire...

They all ohm the same

My dad just told me he was still dealing slightly with his problem, although the new tank and fuel pump helped. Anyhow, he was cleaning up under the hood of the 92 Park Ultra and bumped the postive battery cable (smaller + cable coming out of battery connection) that goes to the alternator and it fell off. Apparently it looked like it had been connected by only a couple threads, therefore not giving a very good charge to the system, which when things started to warm up got to where with too much heat and without the proper voltage didn't allow it to run on all 6.
He went to the slavage yard and picked up a good positive battery harness and put that in. Once that was on the car ran smooth with absolutely no hesitation (he had still been dealing with a slight hesitation since the new pump and tank install -$1100 at a GM dealer in Kansas City, MO in August).
Make sure you check the whole length of the cable, and check all the battery cables.
Good luck.
Martin