Child planets subscribe to the star, and when the star decides to send an update it notifies all its subscribers. Like all Ames messages, we periodically resend the packet (with backoff up to 2min) until we receive an acknowledgment. Thus, as long as at some point both the star and planet are online, the notification will get through, and the child will request the update contents and subscribe to the next version.
The same mechanism is used between galaxies and stars, or in general between any ship and the source of its OTAs (which you can see by running `|ota` with no arguments).