AlwaysOn High Availability - not always kicking in
A deeper dive into the MS's documentation helped us discover the Flexible Automatic Failover Policy (https://docs.microsoft.com/en-us/sql/database-engine/availability-groups/windows/flexible-automatic-failover-policy-availability-group) 

A setting is available to adjust the scenario when the failover should kick in. The default setting is 3.

ALTER AVAILABILITY GROUP AG1 SET (FAILURE_CONDITION_LEVEL = 5);

enabled us to cater for more scenarious, including turning off manually the service. Level 5 encapsulates scenarios/conditions of lesser level values.