See Dropbox API:
401 Bad or expired token. This can happen if the user or Dropbox revoked or expired an access token. To fix, you should re-authenticate the user.
And even better Dropbox Best Practices:
Your app should take precautions in case of revoked access. Access tokens may be disabled by the user (from the account page), revoked by Dropbox administrators in cases of abuse, or simply expire over time.
Unfortunately I can't tell you the time span it takes a token to expire but you should definetely prepare to request new Access Tokens.