  We present late-time optical spectroscopy taken with the Large Binocular
Telescope's Multi-Object Double Spectrograph, an improved ASAS-SN pre-discovery
non-detection, and late-time SWIFT observations of the nearby ($d=193$ Mpc,
$z=0.0436$) tidal disruption event (TDE) ASASSN-14ae. Our observations span
from $\sim$20 days before to $\sim$750 days after discovery. The proximity of
ASASSN-14ae allows us to study the optical evolution of the flare and the
transition to a host dominated state with exceptionally high precision. We
measure very weak H$\alpha$ emission 300 days after discovery ($L_{\rm H\alpha}
\simeq 4\times 10^{39}$ ergs s$^{-1}$) and the most stringent upper limit to
date on the H$\alpha$ luminosity $\sim$750 days after discovery ($L_{\rm
H\alpha} \lesssim 10^{39}$ ergs s$^{-1}$), suggesting that the optical emission
arising from a TDE can vanish on a timescale as short as 1 year. Our results
have important implications for both spectroscopic detection of TDE candidates
at late times, as well as the nature of TDE host galaxies themselves.
