When you turn the steering wheel, you are moving a little lever inside the steering box. That lever pushes on one of two valves, one for the left and one for the right, depending on which direction you turn the wheel. As the rack gear inside the steering box moves, it moves the lever back to the center position and the rack stops moving, until you move the steering wheel again.
I would guess by your description that one of those valves is partially clogged. It could be that one of the power steering hoses has had a little de-lamination on the inside and a chunk of rubber broke free and got into the left valve or some debris got into your power steering reservoir and got stuck in the valve.
I see a remanufactured rack in your future. It is not too difficult to just remove the rack and clean out the valves, but it is very time consuming so the labor may be too high and a reman rack becomes the more economical choice.