  We revisit the calculation of the width for the radiative decay of a $1^{+-}$
heavy $Q \bar Q$ meson via the channel $1^{+-} \to 0^{-+} +\gamma$ in the
covariant light-front quark model. We carry out the reduction of the
light-front amplitude in the non-relativistic limit, explicitly computing the
leading and next-to-leading order relativistic corrections. This shows the
consistency of the light-front approach with the non-relativistic formula for
this electric dipole transition. Furthermore, the theoretical uncertainty in
the predicted width is studied as a function of the inputs for the heavy quark
mass and wavefunction structure parameter. We analyze the specific decays
$h_{c}(1P) \to \eta_{c}(1S) + \gamma$ and $h_{b}(1P) \to \eta_{b}(1S) +
\gamma$. We compare our results with experimental data and with other
theoretical predictions from calculations based on non-relativistic models and
their extensions to include relativistic effects, finding reasonable agreement.
