Accretion plays a central role in the physics that governs the evolution and dispersal of protoplanetary disks. The primary goal of this paper is to analyze the stability over time of the mass accretion rate onto TW Hya, the nearest accreting solar-mass young star. We measure veiling across the optical spectrum in 1169 archival high-resolution spectra of TW Hya, obtained from 1998–2022. The veiling is then converted to accretion rate using 26 flux-calibrated spectra that cover the Balmer jump. The accretion rate measured from the excess continuum has an average of 2.51 × 10−9 M ⊙ yr−1 and a Gaussian distribution with an FWHM of 0.22 dex. This accretion rate may be underestimated by a factor of up to 1.5 because of uncertainty in the bolometric correction and another factor of 1.7 because of excluding the fraction of accretion energy that escapes in lines, especially Lyα. The accretion luminosities are well correlated with He line luminosities but poorly correlated with Hα and Hβ luminosity. The accretion rate is always flickering over hours but on longer timescales has been stable over 25 years. This level of variability is consistent with previous measurements for most, but not all, accreting young stars.