  The robustness of the anomalous Hall conductance, $\sigma_{yx}^{}=
\sigma_{H}^{}$, quantization in the model of a~two-dimensional disordered gas
of massive Dirac electrons subjected to an external orthogonal magnetic field
is investigated in the framework of Kubo--St\v{r}eda formalism. Using the
momentum representation for the averaged one-electron Green functions in
a~magnetic field, an explicit analytical expression for the St\v{r}eda term of
$\sigma_{H}^{}$ is obtained. It is shown that this term is proportional to the
topological Chern number, ${\rm Ch}=\pm 1/2$, if the Fermi level is in the
energy gap. In this case, the total $\sigma_{H}^{}$ takes the half-integer
quantized value, $\sigma_{H}^{}=\pm e_{}^{2}/4\pi\hbar$,that does not depend on
either the magnitude of the disorder or the strength of the external magnetic
field. As an example, we calculated the densities of states and intrinsic
anomalous Hall conductance, $\sigma_{H}^{\rm int}$, of a~two-dimensional
disordered gas of massive Dirac electrons subjected to an external magnetic
field in the self-consistent Born approximation. A numerical analysis of the
field and energy dependencies of these expressions is carried out for various
values of the parameters of the model under consideration. In particular, the
results of this analysis show that the St\v{r}eda term of $\sigma_{H}^{}$ is
susceptible to disorder in a~sufficiently wide vicinity of the point of
transition to the quantization regime.
