Iphone

http://support.apple.com/kb/TS3694

Check for hardware issues

Related errors: 1, 3, 10, 11, 12, 13, 14, 16, 20, 21, 23, 26, 27, 28, 29, 34, 35, 36, 37, 40, 1000, 1002, 1004, 1011, 1012, 1014, 1667, or 1669.

These errors mean that your device or computer may have a hardware issue that's preventing the update or restore from completing.

1. Check that your security software and settings aren't preventing your device from communicating with the Apple update server.
2. Then try to restore your iOS device two more times while connected with a cable, computer, and network you know are good.
3. Confirm that your security software and settings are allowing communication between your device and update servers.
4. If you still see the error message when you update or restore, contact Apple support.

The phone needs servicing, so take it to your local authorized repair shop.

Has the battery been replaced in this iPhone?

You might also try this:

Check your hosts file

After you update iTunes to the latest version, check the hosts file to make sure your computer can contact the update server.

If you’re using a Windows computer, follow the steps in this Microsoft support article (note that resetting thehosts file will affect software services that rely on hosts file redirects). If you're using Windows on a business computer, consult your IT department to be sure applications will work correctly after you reset the hosts file.

If you're using a Mac, follow these steps:

1. In the Finder, choose Applications > Utilities.
2. Open Terminal.
3. Enter this command and press Return:
   sudo nano /private/etc/hosts
4. Enter the password you use to sign in to your computer and press Return. You won't see text appear in the Terminal window when you enter the password. Make sure you use a nonblank administrator password.
5. Terminal will display the hosts file.
6. Navigate using the arrow keys and look for an entry containing “gs.apple.com”.
7. Add the # symbol and a space ("# ") to the beginning of the gs.apple.com entry.
8. Press Control-O to save the file.
9. Press Enter when asked for the filename and Control-X to exit the editor.
10. Restart your computer.
11. Try to update or restore your iOS device again.

The battery may be the issue. If you notice there is a sentence that starts, "If you're using a Windows computer,..."

My iPhone 5 started doing that a few months back (turning off randomly). My device fell under the battery replacement program they're having and since replacing that it hasn't done that. Obviously this may be completely unrelated, but it might be a battery issue so maybe try again after charging it.