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.