Push notifications will lost when app is stoped

Hi,sorry for my poor English.
i have a problem with push notifications.
push receive very well even when device is off after power on app get previously message,but when app force close by user and when user start app again, Messages that have been sent in time to stop the app are not receive.
i think must tell to google play service stop receiving message when app is stop.

Do the messages start arriving after you re-launch the app?