Prior to migrating from Mobile to App Services I could change node.js APIs in real time. Now changes seem to take an undetermined time to go live. I don't know if they're now being compiled or cached anywhere along the way. Ideally I would like to regain the ability to effect immediate change.
Technically, there is a file watcher that watches a subset of the files in your site - when you change one of those files, the site is meant to restart, thus making your change go live. This is configured in the web.config file which is a part of your site.
Make sure that the web.config is configured to watch the files you are interested in.
Restarting the site manually is a backup step that is effective.