since we are using light-speed in our theory we must make an error at the order of S-radii since by definition S-radii is the distance over which the relevant-mass does not let even light escape (read the linked article above and here: All masses behave like black-holes to some extent). SO thats (S-radii) the minimum error or speed anomaly. That is where the singularity of Theory of Relativity exists. Sun’s S-radii is 3 kms hence 3 kms/sec order error on satellites is permitted by Theory of Relativity, at the surface or away from surface the anomaly gradually drops down, as we go far from the effect of gravity, asymptotically to zero. Which is what we are seeing, the speed-anomaly of pioneer is decreasing. Except we do not go close to Sun’s surface hence we do not see 3 kms/sec. We are far away from it and seeing 1.27 mm/sec. (That is our radar is not placed on Sun’s surface but earth’s surface)
400 kms/year is not small, this millimeter accuracy is inbuilt into theory of Relativity, or it would not explain cosmology.