Hi,
Yes , if the controller where APs are terminated, is down all APs terminated on that controller will go down, but there is a mechanism to avoid it,
We can deploy Master-Local, where APs will terminate on Local ( LMS) . we can configure APs such that, if Local is down all APs will go and terminate on the master ( Backup LMS).
We have other deployment models such as, Master-Standby, HA group etc.. to handle single point failure.
Hope got some idea,
Please feel free for any further query on this.