The issue seems to be that the API expects the unit item to be of the form location + /entity/QID instead of concept base URI + QID, where location is the address on which the wikibase instance is accessible (say, the main page).
For Wikidata this is not an issue because users go to wikidata.org and edit there: location and concept base URI coincide (more or less).
However, in a production environment, edits might happen on a temporary URL before pushing the instance to the production URL. For both instances (temporary and production) the concept base URI is the same. Therefore, the unit item should start with the concept base URI.