We're talking about 10 to 15 minutes from a cold start to stall, right? This is usually an failure of a solid state ignition system component. Check for spark using a spark tester or screwdriver. If you have spark, ignore the rest of this answer.
I take it you have a 4-cyl DOCH engine? Look for a faulty crank sensor, cam sensor, or coilpack. If it's a SOHC engine, crank sensor or coilpack. If you lack the equipment needed to tell which is bad (by viewing CKP/CAM signals using a lab scope) try replacing all of the above.
Note that if a CAM or CKP sensor is bad, and you can crank the engine over for more than 30 seconds without the engine starting it should set a code in the computer which you can read with a scan tool. If there is no code, you're likely looking at a bad coilpack.
When replacing any of these components, check that the wiring connectors are in good condition and make a telephone call to verify that an updated wiring connector is not required.