Dropbox API, I can't upload a file to Dropbox (err. 401 Unauthorized)

Polas Здравко is correct; new Dropbox access tokens are not persistent. Dropbox is no longer offering the option for creating new long-lived access tokens. Dropbox is switching to only issuing short-lived access tokens (and optional refresh tokens) instead of long-lived access tokens. You can find more information on this migration here.

Apps can still get long-term access by requesting "offline" access though, in which case the app receives a "refresh token" that can be used to retrieve new short-lived access tokens as needed, without further manual user intervention. You can find more information in the OAuth Guide and authorization documentation. There's a basic outline of processing this flow in this blog post which may serve as a useful example.

And for debugging issues like this, you should print out the HTTPS response body, as it should contain a more useful error message (such as 'invalid_access_token' or 'expired_access_token'). You may need to refer to the documentation for your network client for information on how to access the response body.