P1133 Buick will be replacing HO2S 2nd time in 2yrs, acceleration unsteady

Question

Recent ECM, gas cap replaced and one cycle of "Cataclean" to 4gallons of gas refilled with high test after 22 miles. Plug wires and plugs new.
Symptoms when accelerating with a steady pedal position, the actual speed increases as if I were alternately pressing then backing off on the pedal. On a level road once highway speed is achieved it can be felt to pulse as if I were backing off then on the accelerator. I assure that I am NOT. Idle is smooth with or without A/C when warmed up. Once from a cold start after about 2 min, engine ran rough. When revved once it smoothed without faltering.

Answer 1

Two area that should be suspected, fuel pressure and back pressure. If the fuel pressure is low or fuel filter plugged you would get this faltering you are describing, You can also get this is the catalytic or exhaust is developing  back pressure  Both these situation will set a P1133 and both these situation will also cause cold start up you are experiencing.