We switched from
name: guid(resourceGroup().id, principalId, roleId, uniqueString(resourceName))
to this:
name: guid(resourceGroup().id, principalId, roleId, roleAssigmentName)
We gave the roleAssigmentName a unique name. And this seemed to work.
We could not solve though, why the uniqueString(resourceName) did not produce a unique value on every run?