After reviewing the Shield documentation, it appears that one cannot use self-signed certs in conjunction with Shield: https://www.elastic.co/guide/en/shield/current/ssl-tls.html
The message you're getting implies that your cert is self-signed, rather than signed by a CA... is that the case?
{"@timestamp":"2015-07-03T08:30:43.887Z","level":"error","node_env":"production","error":"Request error, retrying -- DEPTH_ZERO_SELF_SIGNED_CERT"}
{"@timestamp":"2015-07-03T08:30:43.982Z","level":"warn","message":"Unable to revive connection: https://admin_es:akhilesh@localhost:9200/","node_env":"production"}
{"@timestamp":"2015-07-03T08:30:43.983Z","level":"warn","message":"No living connections","node_env":"production"}