Fuel Pump probelm?,99 Ford Taurus, 3.0 Lit

It’s a nuisance at this point, but my opinion is that the pump should be replaced. You did not state the vehicle mileage but the pump is 9 years old and it’s about time. It’s had a good life.
Changing the fuel filter is a must also, and the filter should also be changed every 25-30k miles. Even more often if fuel contamination is suspected since a partially clogged filter can shorten the pump’s life even with the car apparently running fine.

A pump failure can be intermittent sputter or it can be instant and final. There’s no way of knowing.
Considering the constant stress of high pressure and high RPMS that fuel injection pumps are subjected to, it always amazes me that they last as long as they do.