We present late-time optical spectroscopy taken with the Large Binocular Telescope's Multi-Object Double Spectrograph, late-time Swift UVOT and XRT observations, as well as improved ASAS-SN pre-discovery limits on the nearby (d = 90.3 Mpc, z = 0.0206) tidal disruption event (TDE) ASASSN-14li. The late-time optical spectra show Hα emission well in excess of that seen in the SDSS host galaxy spectrum, indicating that the processes powering the luminous flares associated with TDEs can operate for several hundreds of days. The Swift observations reveal the presence of lingering apparently thermal UV (T UV ∼ 3.5 × 10 4 K) and X-ray (T X ∼ 7 × 10 5 K) emission. The characteristic temperatures evolve by, at most, a factor of ∼ 2 over the 600 day follow-up campaign. The X-ray, UV, and Hα luminosities evolve roughly in tandem and at a rate that is consistent with a power-law decay at late times. This behavior is in stark contrast with the majority of optically discovered TDEs, which are X-ray faint and evolve on shorter timescales. Finally we address how the unique properties of ASASSN-14li can be used to probe the relationship between the TDE rate and host galaxy properties.