2003 Ford Taurus

Engine Performance problem
2003 Ford Taurus Front Wheel Drive Automatic 125000 miles

Several times now after driving for an extended amount of time from at least a half hour to an hour, my car, after being turned off for only a short amount of time such as filling the gas tank, will start "jumping" as it is tuned back on and then die without letting me start it again. I took it in and the mechanics could not recreate the problem even after running it hot. The did tell me, however that bank 2 is too lean whatever that means. And that the fuel pressure fluctuates at idle between 31-34 psi which I was told was not enough evidence to replace the fuel pump? Any thoughts would be greatly appreciated Thanku!