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)
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.
If this is working normally, then the issue is most likely with your native notification provider i.e FCM/APNS. Our logAPI (coming soon) will help you figure out if FCM/APNS is failing to forward your messages as notifications to the devices. Please get in touch with us if you want this feature right now.