PI Analysis Service Running/Not Running Tag/Notification
There should be a way to monitor if the analysis service is running, other then just checking if its running from services, or that analysis service is not connected on PSE. There are no specific performance monitor counters that monitor such a thing and analyses would not be possible as if the service is off they would not be ran.
The recommendation is to monitor the PI Analysis Service evaluation count performance counter. Does that work for your needs?