iCould Backup Problem

You might try a forced shutdown to begin with, hold down the top and home buttons together until the device shuts down, then restart it.

First check that your device is correctly connected to the wifi/internet (settings > wifi)

If your back up continually fails, you might try turning off back up on your mobile device (settings > iCloud > storage & backup) and then deleting the backup file from iCloud by swiping the backup file on the mobile device (settings > iCloud > storage & backup > manage…) and then turning back up on again.

If this doesn't help, try turning off some items for back up in a pattern to try to establish if your problem is being caused by specific data on your device.

Being able to back up to the cloud can be very useful, especially if you don't have access to a computer or have infrequent access to one, however unless you specifically need to use iCloud for back up, you will find backing up to iTunes significantly more convenient and possibly more reliable.

Tthere has always been the odd person that has had back up problems and in most cases one of the actions on the list has helped, however there has been a spate of back up problems following the iOS 9 introduction. Again in some cases the actions on the list have helped but in others it hasn't and it seems that there has been some issue with the existing back up file being corrupt or just not properly recognised in conjunction with iOS 9. In some cases repeated attempts to back up have eventually worked, in others it has been necessary to remove the old back up and in some it has been necessary for Apple to have to remove corrupt back up data from the account.

Not sure beyond that, except that once resolved I haven't seen anyone suffer a recurrence.