The first thing I would suggest is going to an Advance Auto or Auto Zone and they will usually run a trouble code check for free. You might have to go to a repair facility to get this done. But, It should not cost much.
There are a lot of possibilities. It does sound like a fuel system management problem. The fuel pump relay could be failing internitantly.
With the mileage on your car, there is a good possiblity that there is something that is dirty enough to effect fuel delivery. The injectors may be clogged or the Idle Air Control Valve, IACV, or emissions equipment such as the Exhaust Gas Return, EGR.
All you can do in these cases is take apart the intake up to and including the throttle body and the aforementioned parts, (which are located on the intake mainifold near the throttle boddy), and clean them.
Another possibility is the the catalytic converter is clogged.

Here is a link that walks through all general possiblities to diagnose the problem that is making your car stall.

http://www.2carpros.com/articles/engine-stalls

I hope this information helps. Get back to us with the trouble codes if you need any help with that.

Answered by DrCranknWrench (expert)
3,292 answers provided

We have been told the fuel pump relay. However we are unable to locate it. Where is it exactly?

Response from ataylor72010
1 question asked

The fuel pump relay is on the right side of the instrument panel in the center support under the radio.

I hope this information helps.

Answered by DrCranknWrench (expert)
3,292 answers provided

Hello, the problem description that ataylor72010 gave in the initial post is exactly the same as what happened to my 2004 xg350 with 120,000 miles. It has now been sitting at the dealership for over a month and they have not been able to fix it. Is there anyway to confirm with ataylor72010 that fixing the fuel pump relay remedied this issue? Thanks

Answered by ah27606
0 questions asked

I sent a message to ataylor and he will get a notice of this post as well. So, hopefully he will respond and let us know if the fuel pump relay fixed the problem.

Answered by DrCranknWrench (expert)
3,292 answers provided

Problem solved---in my case it turned out to be a bad crankshaft position sensor. The car did finally throw that code in the end, P0335. It also had the ignition failure sensor code P0320. Ignition failure sensor was replaced first but the problem remained. When the crankshaft position sensor was replaced, problem went away. Car has been driven about 500 miles since then, with no sign of problem returning. Hope this helps somebody else.

Answered by ah27606
0 questions asked

That is fantastic. I am always so glad to hear things turned out well and got fixed. Good diagnosis on your part. The information will help someone as I now have a little more as I always gain some everday that I work here. I learn information from customers all the time once the problem gets fixed. Diagnosis is hard enough in person. It is amazing that we get it done via texting each other.
So, I thanks you for letting me know how and what it was in the end so I can have that information to pass along in the future.
Information is golden as we say around here and I appreciate it.
Thanks much and take care.

Dr. C

Answered by DrCranknWrench (expert)
3,292 answers provided