Cadillac Repair: 1989 Cadillac Deville sputtersand gasps to a stop, jumper wire, cadillac deville

Question
It's in the shop right now, and the mechanic can't seem to pinpoint the problem. Same problem, when it's cold, runs fine.  After it warms up, dies out like it's out of fuel.  Car does not need a tune up, and the pressure is at 11, which is within the 9 to 13 range according to the mechanic.  Also in the process of changing the fuel filter as I'm writing.  Does this sound like a fuel pump problem?  If so, I will tell him if he doesn't diagnose it first.  
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Followup To

Question -
What could be the problem if the car runs fine on a cold start, but after it warms up(15-30 min. of driving) it begins to die out and sputter to basically a stop?  Then after I let it sit for a few minutes it runs for a few more minutes and does the same thing.  It always restarts.  I took it to a shop or two and they can't seem to tell me what's wrong due to there are no codes to check.  They said I may need a tune up or something with the distributor or even a wire from the battery.  I would apprciate some help with this because I need to get it running again soon.  And how much does a complete tune-up for this vehicle actually cost?

Answer -
When the fault occurs you need to see if you have a loss of ignition to the spark plugs and or a loss of fuel pressure before we can begin a diagnosis.

Answer
What I still do when I have a problem such as this, Is to take my fuel pressure tester and attach it to the fuel line in the engine compartment and tape it on the outside of the windshield and take the car for a drive or get the owners WRITTEN permission to drive the car for a few days so that I can watch the fuel pressure as I drive and see if the pressure drops when the fault occurs. If it does this tells me that I have a fuel pump problem.

I would also put a 10 amped fused jumper wire an attach it to the fuel pump test connector under the hood which puts battery power directly to the fuel pump without having to go thru the computer or the oil pessure switch.

Since it is an 89 year model and most likely has the original fuel pump init anyway, I would replace it anyway.

You can also use the fuel pump test terminal to run the pump all the time while you have the fuel pressure gage on the fuel line and keep an eye on the fuel pressure for an hour or 2 without having to run the engine.