We present a new calibration of the elemental-abundance data for Asteroid 433 Eros taken by the X-ray spectrometer (XRS) aboard the NEAR-Shoemaker spacecraft. (NEAR is an acronym for "Near-Earth Asteroid Rendezvous.") Quantification of the asteroid surface elemental abundance ratios depends critically on accurate knowledge of the incident solar X-ray spectrum, which was monitored simultaneously with asteroid observations. Previously published results suffered from incompletely characterized systematic uncertainties due to an imperfect ground calibration of the NEAR gas solar monitor. The solar monitor response function and associated uncertainties have now been characterized by cross-calibration of a large sample of NEAR solar monitor flight data against contemporary broadband solar X-ray data from the Earth-orbiting GOES-8 (Geostationary Operational Environmental Satellite). The results have been used to analyze XRS spectra acquired from Eros during eight major solar flares (including three that have not previously been reported). The end product of this analysis is a revised set of Eros surface elemental abundance ratios with new error estimates that more accurately reflect the remaining uncertainties in the solar flare spectra: Mg/Si=0.753+0.078/-0.055, Al/Si=0.069±0.055, S/Si=0.005±0.008, Ca/Si=0.060+0.023/-0.024, and Fe/Si=1.678+0.338/-0.320. These revised abundance ratios are consistent within cited uncertainties with the results of Nittler et al. [Nittler, L.R., and 14 colleagues, 2001. Meteorit. Planet. Sci. 36, 1673-1695] and thus support the prior conclusions that 433 Eros has a major-element composition similar to ordinary chondrites with the exception of a strong depletion in sulfur, most likely caused by space weathering.