Is another expiation required for someone who revealed a secret after having sworn to conceal it, and performed the expiation for her oath after the first disclosure, then revealed it again to other people?

This is a binding oath, and it must be fulfilled. Expiation (kaffarah) becomes obligatory upon breaking it.

Fasting is not sufficient for the expiation of an oath except for one who is unable to provide food, clothing, or to free a slave.

If you break the oath once, the oath is dissolved, and you are not required to repeat the expiation for repeated breaking, unless you intended to break it repeatedly or if the wording of the oath implied repetition.