CoughDrop makes use of storage options available in modern browsers, and will not run properly in the Incognito mode available in many systems.
In addition, privacy settings must be configured to allow CoughDrop to store data locally which is used for user identity, offline support and better performance. If you are trying to access CoughDrop in Incognito mode you will most likely see an error message and the app will not load.
Specifically, CoughDrop requires both localStorage and IndexedDB support. For browsers that do not support IndexedDB CoughDrop tries to use a number of fallbacks which generally rely on the same privacy settings needed for localStorage and IndexedDB access.
In Firefox, make sure you are not in private browsing mode. In Preferences go to the "Privacy" section and make sure under "History" you have set "Firefox will" to something other than "Never remember history". For custom settings, you will need to make sure the CoughDrop web site has permission to store data locally.