Do you stop getting certain calls?

No you don't stop getting the same calls in but as you progress and expand the more different types of call you get.

Hope this helps,

Rescue

That call is spawned at a POI: Tram stop, Train station & Hospital so I would check that the underlying POI hasn't been deleted, either your own or an alliance member's.
You can always place additional POIs to see if it will regenerate.