The average stellar mass (M*) of high-mass galaxies (logM*/M⊙ > 11.5) is expected to grow by ~30% since z~1, largely through ongoing mergers that are also invoked to explain the observed increase in galaxy sizes. Direct evidence for the corresponding growth in stellar mass has been elusive, however, in part because the volumes sampled by previous redshift surveys have been too small to yield reliable statistics. In this work, we make use of the Stripe 82 Massive Galaxy Catalog to build a mass-limited sample of 41,770 galaxies (logM*/M⊙ >11.2) with optical-to-near-IR photometry and a large fraction (>55%) of spectroscopic redshifts. Our sample spans 139 deg2, significantly larger than most previous efforts. After accounting for a number of potential systematic errors, including the effects of M* scatter, we measure galaxy stellar mass functions over 0.3 < z < 0.65 and detect no growth in the typical M * of massive galaxies with an uncertainty of 9%. This confidence level is dominated by uncertainties in the star formation history assumed for M*estimates, although our inability to characterize low surface-brightness outskirts may be the most important limitation of our study. Even among these high-mass galaxies, we find evidence for differential evolution when splitting the sample by recent star formation (SF) activity. While low-SF systems appear to become completely passive, we find a mostly sub-dominant population of galaxies with residual, but low rates of star formation (~1 M⊙ yr-1) number density does not evolve. Interestingly, these galaxies become more prominent at higher M*, representing ~10% of all galaxies at 1012M* M⊙ and perhaps dominating at even larger masses.