Android push notifications sent via GCM / FCM are not reliable due to various issues with GCM's underlying architecture [1] [2] [3]. Push notifications may be delayed, rate-limited, lost in transit, or arrive in a different order than which they were sent.
There are alternative push notification gateways you could use instead, which are far more reliable for your time-critical operational needs.
You could try Pushy (https://pushy.me/), a service which offers a highly-reliable push notification gateway for Android apps that works independently from GCM, using its own background MQTT connection.
Full disclosure: I founded Pushy.