  Using soft-graviton theorems a well-known zero-frequency limit (ZFL) for the
gravitational radiation flux $dE^{GW}/d \omega$ is re-derived and extended to
order ${{\cal O}}(\omega)$ and ${{\cal O}}(\omega^2)$ for arbitrary massless
multi-particle collisions. The (angle-integrated, unpolarized) ${{\cal
O}}(\omega)$ correction to the flux turns out to be absent in the case of
two-particle elastic collisions. The ${{\cal O}}(\omega^2)$ correction is
instead non-vanishing and takes a simple general expression which is then
applied to bremsstrahlung from two-particle elastic collisions. For a
tree-level process the outcome is finite and consistent with expectations.
Instead, if the tree-level form of the soft theorems is used at sub-sub-leading
order even when the elastic amplitude needs an all-loop (eikonal) resummation,
an unphysical infrared singularity occurs. Its origin can be traced to the
infinite Coulomb phase of gravitational scattering in four dimensions. We
briefly discuss how to get rid, in principle, of the unwanted divergences and
indicate --without carrying out-- a possible procedure to find the proper
correction to the naive soft theorems. Nevertheless, if a simple recipe
recently proposed for handling these divergences is adopted, we find
surprisingly good agreement with results obtained independently via the eikonal
approach to transplanckian-energy scattering at large (small) impact parameter
(deflection angle), where such Coulomb divergences explicitly cancel out.
