Hi nadi6677,
We understand that the Life360 app keeps showing its on battery saver. We will do our best to assist.
Since the app is working as expected on other devices, let's make sure the Life360 app and the iPhone's software are up-to-date. Before updating the iPhone's software, be sure that you have a current backup. For steps on backing up and updating, check out this link: Update your iPhone, iPad, or iPod touch
Afterward, make sure the app is updated by following the steps here: Update apps or use automatic downloads
If issue persists, reach out to Life360 support for further assistance.
Take care.