If you want to get the group members to be persisted, you have to use an asterisk:
gPersistInfluxChange* : strategy = everyChange,everyHour,everyDay
Without the *, the item itself will be persisted, but not the members. Keep in mind, if using the *, the group item itself won’t be persisted, so, if you want both group members and group item itself to be persisted, use two definitions in .persist file.