Different payment card associations use different account updater models. This fact should be kept in mind by recurring billing companies (especially, by companies, dealing with systems, which follow different account updater models).
Many payment gateways follow the so-called integrated model. Under this model a merchant sends transactions to be processed by a payment gateway, as usual. If an update for some account is available (from the issuer), the payment gateway adds updated account information to the response to the respective transaction before sending it back to the merchant.
American Express follows the so-called subscription-based model. Under this model a merchant can get updated account information on a regular basis. Once some update becomes available, a merchant gets a respective notification.
Visa and MasterCard follow the so-called file-based model. Under this model a merchant sends a file with account numbers and gets back a file, containing updates for those accounts, for which they are available.
To learn more about account updater models, read the respective article on Paylosophy.