One thing that plagues single pivot brakes is spring friction at the arms. As the arms move in and out the spring moves up and down slightly, sliding against where it meets the arm. A bit of friction there can cause the arm to open less throwing off the centering when open. So make sure the place where the spring meets the arm is reasonably clean (wiped, not washed), then put a drop or light oil, like a teflon dry lube there.

Now work the brake to make sure it's opening consistently, then center by loosening the mounting nut, rotating the pivot and re-tightening.