Car will not pass New York State inspection

Miles in the last four years. The battery died and was replaced at a caddy repair shop. The check engine lite came on when I brought the car in for an inspection, they replaced a O2 senser and told me to drive the car. I have now driven this car over 4000 mile driven in the last 4 yrs. Battery was replaced 2 yrs. Ago. New battery was recharged and has not been a problem, no check engine lite was on when I brought it in --- the lite came on and they replaced an O2 sensor, but did not pass inspection. The check engine lite was not on. I was told to drive the car -- I have now driven 400 miles, taken the car back every 100 mile to have checked -- and am being told to keep driving the car. The reggy is now up and I cannot continue to drive in circles.