When the device is down, the threshold alerts on the device does send the re-notifications. In case the device is down for a long time and the threshold alert was active when the device went down, it will re-notify the user for the alert until the device is active again and the threshold didn't subside. For the service checks, this gets controlled by the host down and the re-notifications on all failed service check doesn't happen if the device is down. Similar thing can be worked on the thresholds which will prevent alerting which doesn't mean anything.