I had it working earlier, but now, attempts to edit the file in aseprite just give me an error message saying "Websocket failed to send data". 

Heyo, guess it broke or something. Perhaps you have shut down blender side plugin at some point, or it crashed in a specific way that prevents it from launching. Could you check what the connection status is in the addon panel in blender, and if there’s any messages in the console (Menu bar > Window > Toggle System console).

Otherwise please specify your OS, blender, aseprite, and plugin versions; whether you updated the plugin, and detail/record how you’re launching it.