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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.
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.
Might not be the same problem, but I was having similar issues and this was the problem.
I didn't realize my iphone wasn't properly connecting to my home network after one of the updates. I always thought I was using the wifi because when I looked under settings my network was listed to the right of wi-fi.Apparantly it was trying to connect over and over again but never had a solid connection. Not sure what happened, but this is what fixed it.
Go to settings>Wi-Fi>click on your network, then select "Forget this Network"
>then click back to the wifi network list and select "Other" and manually enter your Network name exactly as it appears (Ex: 2WIRE633) and select the type of security you have on it. (Ex: WPA2Personal)
Next see if you get a check mark next to your network and try to Backup to icloud again.
Mine was not backing up, and the "back up now" button would not respond, I think it was greyed out. My wife's phone had been doing the auto back up OK, but not mine. I did the hard reset just now as recommended, restarted and touched the "backup now" button, and it backed up with no problems. I bet it will back up automatically now, but I may need to just do a hard reset from time to time.
I wonder if backing to the cloud is as sure a thing as backing up manually to iTunes, with a hard wired USB connection to the computer?