  We perform quantum electrodynamic calculations of the ionization energy of
the $1s3d$ states of the $^4$He atom, including a complete evaluation of the
$m\alpha^6$ correction. We find a large contribution from the nonradiative part
of this correction, which has not been accounted for in previous
investigations. The additional contribution shifts theoretical predictions for
ionization energies by about 10$\,\sigma$. Despite this shift, we confirm the
previously reported systematic deviations between measured experimental results
and theoretical predictions for transitions involving $3D$ states. The reason
for these deviations remains unknown.
