Dropbox have a new way of connecting a user to their files. It might be worth investigating this as a replacement for the current API.
Greg from Dropbox API support here. (If this isn't the right address for this, please forward it along appropriately. Thanks!)
First of all, I'd like to thank you for developing the Dropbox functionality for Moodle and enabling Moodle users to easily use their Dropbox files in Moodle. I just wanted to reach out and let you know about something we recently released that I think you and your users might be interested in. It's called the Dropbox Chooser:
The Dropbox Chooser is the fastest way to integrate Dropbox into your web app. It lets Dropbox users select files from their Dropbox and pass them to your app without having to go through a heavyweight auth flow.
We'd love if you'd consider integrating the Dropbox Chooser into Moodle in place of the existing Dropbox repository module. Using the Dropbox Chooser would be beneficial for your users in several ways:
a) The Dropbox Chooser doesn't have any notion of development/production status, so anyone who wished to use it wouldn't have to apply for production. (They would still need to register their own Chooser app to get their key, but it should still be faster and easier.)
b) The Dropbox Chooser uses a new access type wherein only the files specifically chosen can be accessed by the app, minimizing both any security issues with asking for full access, as well as usability issues with asking for only app folder access.
Anyway, thanks for reading! If you have any questions, please don't hesitate to reply and ask!