Bug: An error occurs when creating a local copy of a service for editing in ArcMap 10.1
The error, "A local copy could not be created. The requested capability is not supported," is returned when attempting to create a local copy of a service for editing with the Create, Query, and Update operations enabled.
This is a known issue.
The Delete operation must also be enabled in the feature service properties. All the editing operations must be enabled to successfully create a local copy of a service for editing without an error.