  We evaluate the low-temperature conductance of a weakly interacting
one-dimensional helical liquid without axial spin symmetry. The lack of that
symmetry allows for inelastic backscattering of a single electron, accompanied
by forward-scattering of another. This joint effect of weak interactions and
potential scattering off impurities results in a temperature-dependent
deviation from the quantized conductance, $\delta G \propto T^4$. In addition,
$\delta G$ is sensitive to the position of the Fermi level. We determine
numerically the parameters entering our generic model for the
Bernevig-Hughes-Zhang Hamiltonian of a HgTe/CdTe quantum well in the presence
of Rashba spin-orbit coupling.
