The electrochemical performance of aluminum-sulfur batteries is beset by poor stability and sluggish charge-storage properties. To address these issues, carbon allotropes have been used as electrode fillers, but successful outcomes remain inexplicably elusive. Here, a composite of sulfur and small-diameter single-walled carbon nanotubes was studied as a cathode for AlCl3:[EMIM]-based aluminum batteries. The presence of carbon nanotubes, while enabling a high capacity (1024 mAh g-1) with slower decay and reducing the electrolyte-to-sulfur ratio, is insufficient to fully stabilize the cell's performance. In fact, the main obstacle is in the interaction between sulfur and chloroaluminate ions. As we show, there is a gradual buildup of insoluble and poorly conductive discharge products that inhibit the diffusion of electroactive ions and, ultimately, cause capacity decay. Overall, this work sheds light on the carbon-sulfur-electrolyte interactions and their role on the underlying charge-storage mechanism of aluminum-sulfur batteries.