Assuming both client and publisher's internal systems are intact, then you have two attack vectors:
There's the false positive attack vector, where you can shut down the client's network access and force the secret to be prematurely leaked.
There's the false negative attack vector, where you can shut down the trusted publisher's network access, and indefinitely keep the secret ``safe''.
However, in general, the first attack is not as worrisome as the second for these kinds of application. The second is more worrisome, and there's many ways to distribute the trusted published using some crypto threshold scheme such that as long as no more than some threshold of the trusted publishers are shut down, the secret will be released in case of client shutdown.