If you only want your app to connect to your own account, and for more than a few hours without manual intervention, you should use the OAuth app authorization flow and process it once yourself to get a "refresh token" for your own account. That particular refresh token will always be only for your own account and will not expire automatically (though you can revoke it if/when needed).
If you're using the official Dropbox Java SDK, you can find an example Android app here.
Note though that the API was designed with the intention that each user would link their own Dropbox account, in order to interact with their own files. While it is technically possible to always connect to just one account for all users, we do not officially support this, for various technical and security reasons. For instance, as a matter of security, you should not distribute your own access token or refresh token to other users, e.g., inside of a client-side app like an Android app.
