In our case it was a permissions issue. We submitted a Daycare ticket and after reviewing our logs in the following location, we identified the user that needed to have permissions adjusted.
AEM > Tools > Deployment > Replication > Agents on Author > {our environment} MP Replication Agent0 Default > View log
Once that change was made, we were able to get our custom metadata and corresponding custom search facets to publish to Brand Portal as expected. I'm not sure if that will help in your case but that's the breakthrough solution on our end.