The same happens to my addon. Worked fine up to Firefox 40. I found that is a problem with the new jpm and paths. Now relative paths are needed and other changes too.
For example:
Previous code, not working with FF40:
tabs = require(‘tabs’);
data = require(“self”).data;
…
contentURL: data.url(“html/popup.html”)
New code working:
tabs = require(‘sdk/tabs’);
data = require(‘sdk/self’).data;
…
contentURL: data.url(“./html/popup.html”)