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I think it's more likely that he is using some kind of default defender setting which drops data at some point to save battery. But yes, people should not be using apps they don't understand.
Are you sure none of these contacts show up in Google Contacts (gmail, "all contacts")? The fact that they are listed in an "all contacts" folder makes me suspect that you might have not checked properly. Also, is there on your phone another type of account, perhaps manufacturer-only that syncs contacts to the cloud? What app are you using for sending texts? Do they show up if you use a different text-sending app?
You might be underestimating your kids' mobile phone skills. Maybe they figured out how to do that, or did it by mistake, and a nabaztag app, for example, sounds pretty exciting to a kid not knowing that they require the actual nabaztag device to use it.
