  We report the discovery in TESS data and validation of HD 56414 b (a.k.a.
TOI-1228 b), a Neptune-size ($R_{\rm p} = 3.71 \pm 0.20\, R_\oplus$) planet
with a 29-day orbital period transiting a young (Age = $420 \pm 140$ Myr)
A-type star in the TESS southern continuous viewing zone. HD 56414 is one of
the hottest stars ($T_{\rm eff} = 8500 \pm 150 \, {\rm K}$) to host a known
sub-Jovian planet. HD 56414 b lies on the boundary of the hot Neptune desert in
planet radius -- bolometric insolation flux space, suggesting that the planet
may be experiencing mass loss. To explore this, we apply a photoevaporation
model that incorporates the high near ultraviolet continuum emission of A-type
stars. We find that the planet can retain most of its atmosphere over the
typical 1-Gyr main sequence lifetime of an A-type star if its mass is $\ge 8 \,
M_\oplus$. Our model also predicts that close-in Neptune-size planets with
masses $< 14 \, M_\oplus$ are susceptible to total atmospheric stripping over 1
Gyr, hinting that the hot Neptune desert, which has been previously observed
around FGKM-type stars, likely extends to A-type stars.
