The issuance of a refresh token with the client credential grant has no benefit.
That is why the RFC6749 section 4.4.3 indicates A refresh token SHOULD NOT be included. Thus its issuance is at the discretion of the authorization server.
From my point of view an authorization server should never issue a refresh token with the client credentials grant as the access token issuance process will take an additional and unnecessary step:
- The issuance of he access token with the client_credentials grant type is done on the first request.
- The issuance of he access token with the refresh_token grant type is done after at least two requests, depending on the way you issued to first access token.