The best way to do this with BigFix but without using a custom app that makes use of the REST API would be using Web Reports which has a capability to send emails based upon the results of a custom report changing, which is generally powered by session relevance.
You can test session relevance in web reports by visiting:
This can be used to determine which computers are relays:
This should give the names of all relays:
(name of it | "") of bes computers whose(relay server flag of it)
This should give the names of all relays who’s last report time > 30min:
(name of it | "", last report times of it) whose(now - item 1 of it < 30 * minute) of bes computers whose(relay server flag of it)
Getting relays in which the client is functional but the relay service is stopped is not as easy and would require an analysis property be active that reports on this info.