Actually it's the idle air bypass valve that the other posts are referring to. This is attached to the intake manifold just opposite the throttle body, attached by 2 allen head bolts. It regulates air flow at idle with the throttle closed. One way to diagnose this is to press lightly on the throttle at idle, see if the car stays running.
If the valve is not opening enough or staying open the engine will stall. Opening the throttle slightly yourself serves the same purpose. If the car still stalls with the throttle open then the problem is likely to be elsewhere.
Have you pulled any codes or noticed any temperature issues? The few min running time seems like a temperature issue with a component, especially with the diminishing run time for each attempt.
If you do pull the idle air bypass, watch the lower bolt doesn't fall into the engine valley, right along with the allen key. You might want a magnetic parts grabber handy for this one.