It seems that adjusting the timeout setting in the Deluge plugin can cause you to get locked out of the webUI permanently. I had tried setting it to -1, intending for this to disable the timeout completely. Instead, I am immediately asked for my password again and again. I haven't figured out how to resolve it other than uninstalling and reinstalling the plugin.
Edit: Apparently it's not just me - https://twitter.com/bentkwillis/status/594921547900452864