  A single pair of helical edge states as realized at the boundary of a quantum
spin Hall insulator is known to be robust against elastic single particle
backscattering as long as time reversal symmetry is preserved. However, there
is no symmetry preventing inelastic backscattering as brought about by phonons
in the presence of Rashba spin orbit coupling. In this letter, we show that the
quantized conductivity of a single channel of helical Dirac electrons is
protected even against this inelastic mechanism to leading order. We further
demonstrate that this result remains valid even when Coulomb interaction is
included in the framework of a helical Tomonaga Luttinger liquid.
