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Efforts to discover and characterize habitable zone planets have primarily focused on Sun-like stars and M dwarfs. K stars, however, provide an appealing compromise between these two alternatives that has been relatively unexplored. Understanding the ultraviolet (UV) environment around such stars is critical to our understanding of their planets, as the UV can drastically alter the photochemistry of a planet's atmosphere. Here we present near-UV and far-UV \textit{Hubble Space Telescope}'s Cosmic Origins Spectrograph observations of 39 K stars at three distinct ages: 40 Myr, 650 Myr, and $\approx$5 Gyr. We find that the K star (0.6 -- 0.8 M$_{\odot}$) UV flux remains constant beyond 650 Myr before falling off by an order of magnitude by field age. This is distinct from early M stars (0.3 -- 0.6 M$_{\odot}$), which begin to decline after only a few hundred Myr. However, the rotation-UV activity relation for K stars is nearly identical to that of early M stars. These results may be a consequence of the spin-down stalling effect recently reported for K dwarfs, in which the spin-down of K stars halts for over a Gyr when their rotation periods reach $\approx$10 d, rather than the continuous spin down that G stars experience. These results imply that exoplanets orbiting K dwarfs may experience a stronger UV environment than thought, weakening the case for K stars as hosts of potential "super-habitable" planets.