This is clearly related to power management, and you need push notifications.
See the following for more information:
https://wiki.linphone.org/xwiki/wiki/public/view/Flexisip/D.%20Specifications/Push%20notifications/
https://wiki.linphone.org/xwiki/wiki/public/view/Lib/Features/Push%20notifica
Maybe your problem is related to power management. iphone and android both
can be configured to save power when you are not using an app. The
operating system does this to conserve battery drain. Also I dont know
about Linphone specifically, but there is something called push... that can
help i
