In various embodiments of the present invention, tiered command-propagation methods are employed within client computers to ensure that monitoring-and-management-related commands are reliably propagated from server computers to client computers. When possible, command propagation is initiated by server computers through a notification process. When the notification process is inoperable, client computers poll one or more monitoring-and-management server computer for commands. When a failed or interrupted notification process is subsequently restored to operability, client computers automatically discontinue command polling and resume relying on server notification for command propagation.