Delete iCloud backup iOS 9

Solution 1:

There is a solution for that on the internet I believe. http://macreports.com/icloud-this-backup-cannot-be-deleted-at-this-time-error-fix/

Try restarting your phone and reconnecting to the wifi or even logging out and logging back in to your Apple ID. If it still doesn't work, you might want to consider doing that from a computer. You can follow the instructions here. https://support.apple.com/kb/ph12792

Remove a backup using your Mac

1. Choose Apple menu > System Preferences, click iCloud, then click Manage.

2. Click Backups on the left, select an iOS device on the right whose backup you don’t need, then click Delete.

3. If you don’t see Backups on the left, your iOS devices don’t have iCloud backups. For more information, see Back up your iOS device to iCloud.

Remove a backup using your Windows computer

1. Open iCloud for Windows, then click Storage.

2. Click Backups on the left, select an iOS device on the right whose backup you don’t need, then click Delete.

3. If you don’t see Backups on the left, your iOS devices don’t have iCloud backups. For more information, see Back up your iOS device to iCloud.

Solution 2:

In addition to @RyanJin's answer, I spoke with a senior apple support advisor about this issue when my problem persisted. While on support, they stated that:

Once an iCloud backup restore has been activated for a device, a restore-block is placed on the backup for 48 hours. During this time, the backup cannot be deleted.

Prior to discovering this rule they had me:

1. Logout of icloud
2. Restart the phone
3. Log back into icloud
4. Attempt deletion again