Updating a staging repository's description requires a PUT request to /service/local/staging/repository/<repo-id>. From the source code it can be seen that this requires update privileges to "nexus:stagingprofilerepos".
However, the security.xml file for staging does not provide an update privilege for this resource, it only has read resources.
Consequentially, it seems that you can only update staging repository descriptions if you have administrator role in the server.
If my assessment above is correct then this can be fixed by adding a privilege definition in the security.xml file which allows update.