No. If someone other than you knows the secret, it is no longer a secret, period.
The secret is a formula to enternal life. That is the big secret! The little secret is that Cass`dad is related to a jester.
The secret being discussed is the secret of life. Levertov never sheds any light on what the particular secret might be, but implies that it was so simple, none of them could even remember it :)
Because most secrets are things that should be released to the public for their own good
The same way you keep anything a secret - you tell no one you can't trust.