To let iCloud back up the child iPhone automatically every day, please make sure the following are true:
You have turned on iCloud backup in Settings > Apple ID > iCloud > iCloud Backup.
Your device has an active Wi-Fi network connection and there is enough iCloud storage for the backup to complete.
Your device must be plugged into a power source and the screen must be off.
Please Note: You can also force a manual backup (see #4 below).
If the child iPhone fails to meet these requirements, it is unable to back up data to iCloud. And above all, no Wi-Fi connection and lack of iCloud storage are the two most common reasons why an iPhone won't back up to iCloud.
When the child iPhone is unable to back up data to iCloud, here is what you can do to fix it.
1. Make sure iCloud backup is turned on.
On the child's device open Settings > Apple ID > iCloud > iCloud Backup. Make sure that iCloud Backup is turned on.
2. Check Wi-Fi Connection and iCloud Storage
First of all, you should make sure the child iPhone has a strong Wi-Fi network connection, especially when you want it to back up automatically at night.
Then you should check the available iCloud storage of your account:
Tap Settings > Apple ID > iCloud > Storage and you'll see the available iCloud storage.
Go to Manage Storage > Backup. It will estimate the size of your next backup.
If there is not enough iCloud storage for the next backup, you can tap Delete Backup to make room for the new one or make a smaller backup by choosing less data to back up.
Otherwise, you need to purchase more iCloud storage: Settings > Apple ID > iCloud > Storage > Manage Storage > Change Storage Plan.
3. Check to make sure the device is plugged into a power source and the screen is off.
The child's device must be plugged into a power source (charger or computer) and the screen must be off or locked. Note that the device must be powered on.
4. Backup iPhone to iCloud Manually
This is helpful when you get the message saying "your last backup couldn't be completed" or your iPhone won't back up to iCloud automatically.
Open Settings app on your iPhone;
If you are using iOS 10.2 or latter, tap Apple ID > iCloud > iCloud Backup > Back Up Now;
If your iPhone is running on iOS 10.1 or earlier, tap iCloud > Backup > Back Up Now.