I am betting someone here will have a great suggestion on what might be wrong.
My mom has 2OOO Buick LeSabre 120,000 ish miles. At 81 she does not have any interest in a new car but I need to be sure this one is safe and right now it is not.
It is in the habit of stalling, highway speeds, city speeds and once as she pulled to a stop. It does not start running rough or any sign just all of a sudden it is slowing down and you realize it stalled out. When I restarted it she ran a little rough for a few seconds then runs fine.
Other than that it has nothing wrong she keeps up on all the regular maintenance.
We had the electronic ignition computer thing replaced and they have gone through and cleaned plugs and filters checked all the plug wires.