Some Android devices, such as Samsungs phones, limit background activity of applications which can result in push notifications not coming through.
Usually, when the School Life application is open, or has been opened and has been closed recently, the background services will remain active, to allow the application to be informed that push message has been received.
However, some versions of Android will limit this background activity in the aim to save battery or restrict access for the application, which interrupts how push notifications work.
You can resolve this yourself, however it will differ depending on your device.
Many Android devices come with their own form of battery management, for power saving (Samsung & Sony for example). These options restrict the phones performance and certain features to help reduce battery drain and prolong the phones battery life. This, although useful, can also limit background tasks such as the push notifications.
Try disabling/modifying this option to allow notifications to come through.