  Quantum electrodynamical (QED) calculations of ionization energies of the
$1snd\,D$ states are performed for the helium atom. We reproduce the previously
known relativistic and QED effects up to order $m\alpha^5$ and extend the
theory by calculating the complete $m\alpha^6$ correction. The total
contribution of the $m\alpha^6$ effects is shown to be much smaller than
previously estimated, due to a large cancelation between the radiative and
non-radiative parts of this correction. As a result of our calculations, we
confirm the previously reported deviations between measured transition energies
and theoretical predictions for the $nD$--$2S$ and $nD$--$2P$ transitions.
Possible reasons for this discrepancy are analyzed.
