1999 Buick Century Engine "cut out"

Engine Performance problem
1999 Buick Century Automatic 62,500 miles

This vehicle will run well for awhile and then the engine will "cut out" and stall while driving. Very dangerous on the highway. After sitting for a few minutes I can start it up -- drive awhile and it will "cut out" again. It has cut out 3 times within the distance of less than 6 miles.
When the fuel tank was less than one quarter full, I put fuel line cleaning fluid in the tank and filled the tank with high test gasoline (about 15 gallons).
The problem continued.
I took it to the Buick Dealer where a diagnostic test was run. Nothing abnormal was appeared.
The dealer checked the fuel filter which also appeared OK for another 10 - 15,000 miles.
No charge for the above service.
I hope its not the fuel pump (a $500 part -- which is a lot for a retiree on a fixed income).
Any ideas would be appreciated.`
Thanks,
Bill Stewart
Military Historian
Google - saipanstewart. Com
and open on "home" for interesting W W II stories.