A store-and-forward email system will not deliver messages until:

In a store-and-forward email system, messages are stored on a server until they can be successfully sent to the recipient. This means that the system will retain emails temporarily, rather than attempting to deliver them immediately. The process typically involves the server storing the email until a connection is available to forward the message to the recipient.

The correct response indicates that the host, which refers to the email server responsible for managing the email traffic, must request the information to process the delivery of the email. This clarifies that it is the server's responsibility to ensure that emails are sent out only when the necessary conditions for successful delivery are met.

In contrast, other options do not accurately reflect how the store-and-forward process operates. Simply checking email or downloading data involves actions taken by the recipient's email client but do not initiate the delivery process per se. Similarly, while the restoration of the network is a necessary condition for successful communication, it does not pertain directly to the specific functioning of a store-and-forward system, as the email remains undelivered until actively requested by the host.