The mixed-derivative skewness S_uθ of a passive scalar field in high Reynolds and Prandtl numbers decaying homogeneous isotropic turbulence is studied numerically using eddy-damped quasi-normal markovian closure, for Re_λ ≥ 10^3 up to Pr = 10^5. A convergence of S_uθ for Pr ≥ 10^3 is observed for any high enough Reynolds number. This asymptotic high Pr regime can be interpreted as a saturation of the mixing properties of the flow at small scales. The decay of the derivative skewnesses from high to low Reynolds numbers and the influence of large scales initial conditions are investigated as well.