iPod touch cannot receive iMessages when asleep.
iPod touch cannot receive iMessages when asleep, for instance, in the morning when the device has been unused all night. Once the device has been woken up (by pressing home button and logging in), the messages will come through. The three 6th get iPod Touches and our WiFi iPad suffer from this. Why? iPhones do not have this limitation.
iPod touch, iOS 9.2.1