I would suggest you to reset Windows store cache memory and check if it helps.
You can follow the steps to do so:
a)On the desktop screen, pressWindows and R key to open run box.
b)Type WSReset.exe and hitEnter.
Try to install Windows 8.1 again from Store and check if it resolves the issue. If not, proceed to the second method.
If you have any third party security software installed on the computer, let’s uninstall it and check if that’s the cause for the failed installation.
Important Note: Security software can help protect your computer against viruses and other security threats. In most cases, you shouldn't disable your antivirus software. If you have to temporarily
disable it to install other software, you should re-enable it as soon as you're done. If you're connected to the Internet or a network while your antivirus software is disabled, your computer is vulnerable to attacks.
If the issue still persists, please try to reset your Windows 8(Note:Backup your data firstly), and then retry to update to Windows 8.1.
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