If you aren't receiving expected Push Notifications on your device, this can be due various reasons. You'll need to figure out if it's an issue on Ably's side or some issue with your device's registration with FCM/APNS.
The following steps can help you get a better idea of what may be happening:
1. Find your device's identifier (deviceId, clientId, etc)
In the Ably dashboard, go to the Notifications tab and use the device inspector to inspect that device ID.
If the state is FAILED an error should also be displayed.
The most common error is registration expired where the user uninstalled the app or disabled notifications.
If the device is ACTIVE then you can use the push inspector to test notifications to a device:
2. Use Ably's REST API to publish a push notification directly to your device using the 'deviceId' (or any other supported identifier) to see if this part of the message flow is working
3. You can also look at the stats on your Ably account dashboard to understand if the message was delivered at all from Ably's Data Stream Network.
You will need to have a tab open on the dev console tab to inspect the logs at the time or you can subscribe to the [meta]log:push channel instead.
From any errors there you should see an FCM or APNS reason why the notification failed. If no logs are raised it means the notification succeeded.
If this is working normally, then the issue is most likely with your native notification provider i.e FCM/APNS.