Improved connectivity verification is disclosed. A root in a point-to-multipoint network can establish parameters for a connectivity-verification session with each endpoint in the network. The root then sends verification-request messages to each endpoint in accordance with the parameters. Each endpoint signals an alarm (e.g., sends a reply to the root) if the verification-request messages are not received at the endpoint in accordance with the established parameters. In this manner, endpoints send verification-reply messages to the root much less frequently, greatly reducing the congestion at the root and greatly reducing the chance that the root gets congested or even overwhelmed when the network includes large numbers of endpoints.