The signatures of planets hosted by M dwarfs are more readily detected with transit photometry and radial velocity methods than those of planets around larger stars. Recently, transit photometry was used to discover seven planets orbiting the late-M dwarf TRAPPIST-1. Three of TRAPPIST-1's planets fall in the Habitable Zone, a region where liquid water could exist on the planetary surface given appropriate planetary conditions. We aim to investigate the habitability of the TRAPPIST-1 planets by studying the star's activity and its effect on the planets. We analyze previously published space-and ground-based light curves and show the photometrically determined rotation period of TRAPPIST-1 appears to vary over time due to complicated, evolving surface activity. The dramatic changes of the surface of TRAPPIST-1 suggest that rotation periods determined photometrically may not be reliable for this and similarly active stars. While the activity of the star is low, we use the premise of the cosmic shoreline to provide evidence that the TRAPPIST-1 environment has potentially led to the erosion of possible planetary atmospheres by extreme ultraviolet stellar emission.