We ran into the same issue, it's more pronounced if your community is full site SSL enabled (HTTPS). Most browsers won't allow the CSS to load from your local machine as they see this as insecure.
The workaround for this unfortunately is a bit involved and requires you setting up an Apache Web Server on your local machine, creating symbolic links to the required directories in the SDK files and configuring SSL for the local web server.
For example instead of http://localhost:9000/skin_name/skin.css our staging environment now points to https://localhost/skin_name/skin.css wich works.
Can you confirm if your staging site is https:// enabled?
Yes it is SSL enabled. However I dont believe that is the issue. It did allow me to use localhost:9000/ as the skin URL when I followed the steps because I saw in the head tag it was using that URL, and going to that URL had content - it was just the wrong folder (web/ folder). I think this is is because I cannot set up responsive options to point to the correct folder, because running "li set-responsive-options" fails because it thinks our custom skin is not a responsive skin, because we do not have all of our skins in Studio downloaded into the SDK, so it thinks the skin our custom skin depends on (Support Theme) is not based on a responsive skin.
