I had a similar problem with my 15 Neon Sport. It would start and run fine, but once it ran for awhile it would just die for no apparent reason. after it sat for awhile (usually while it was going onto a flatbed) it would start right up. the fuel pressure tested fine, but i was told the pump might be bad. i changed it, and it fixed that problem permenantly. it turns out that while it runs and tests out fine while cold and sometimes at idle after running for awhile, when the pump warms up and/or you try to hit give it some gas, the pump seizes, and drops the pressure