If your push notifications are delayed, please read here:
Storm of Wars integrated with the Push Notification service provided by all the platforms (Apple / Android / Windows), and the notifications are delivered by the platform to your device, which is why you can turn it on and off through your device's Settings and also means if the network between the platform's Notification Server and your device has a hiccup, the delivery could be delayed.

Therefore, to prevent it from happening, it's very important that you are connected to a reliable network and that your device's signal is strong. Full wifi bars or mobile (cellular) data coverage alone is not always enough to guarantee a solid connection, because local networks can slow down and get overburdened at times. This is especially true if you are streaming videos, play in a moving vehicle or on underground public transport.

If you receive no push notification at all, please follow the instructions:
1) Go to the device's Push Notification center, and turn off the notification for Storm of Wars. 
2) Uninstall the game 
3) Turn your phone off, wait for 1 minute, and turn it back on 
4) Install the game, don't open it yet. 
5) Go to the device's Push Notification, and turn on the notification for Storm of Wars. 
6) Then open the game and restore your account. 

Moreover, in Step (5), if the Push Notification is already enabled when you check it in the Device's setting, please manually disable and re-enable the Push Notification for Storm of Wars before launching the game.