When a user reauthorizes a page, it renews that user's authorization token in Social. At least one valid token must be available on a page for posting to work successfully.
Facebook error example: "We could not automatically post a message to Facebook as requested, because an exception occurred. The exception was: "Posting failed with all admin tokens.”
To avoid the "Posting failed with all admin tokens” error, have as many admins of the page as possible reauthorize. To reauthorize, go to Social > Settings > Facebook Permissions, and click the Re-Authorize button. If only one token is currently valid/authorized on a page—for example the token for a user named Jen—there are no other tokens that could be used for posting if Jen’s token becomes invalid. If Jen's token becomes invalid for (for example, she changed her password on Facebook, the token has expired automatically), posts fail.
As a best practice, everyone in Social who is an admin of a given social property should reauthorize their pages. Then, if for example Jen’s token is no longer valid, Social tries posting with another user's token. If that second person's token is no longer valid, then Social tries the next user's token. And, it continues to try tokens until it finds one that's valid. While there is no guarantee that you won't experience the same error, it reduces the likelihood if more users reauthorize the same page, creating valid tokens for each user.
Authorization/reauthorization to renew and create valid tokens for other types of social properties are handled here.