  We complete the study of two-loop infrared singularities of scattering
amplitudes with an arbitrary number of massive and massless partons in
non-abelian gauge theories. To this end, we calculate the universal functions
F_1 and f_2, which completely specify the structure of three-parton
correlations in the soft anomalous-dimension matrix, at two-loop order in
closed analytic form. Both functions are found to be suppressed like O(m^4/s^2)
in the limit of small parton masses, in accordance with mass factorization
theorems proposed in the literature. On the other hand, they are unsuppressed
and diverge logarithmically near the threshold for pair production of two heavy
particles. As an application, we calculate the two-loop anomalous-dimension
matrix for q q_bar --> t t_bar near threshold and show that it is not diagonal
in the s-channel singlet-octet basis.
