Note that the answer accepted for this problem appears to only be applicable to systems using some form of full disk encryption.
I just tried to install windows 8.1 on my laptop, but it fails to install with the message:
Sorry we couldn't complete the update to Windows 8.1.
We restored your previous version of Windows to this PC
0xC1900101 - 0x20017
The update installed just fine on my desktop. The difference between the two machines is that the desktop has media center install, and isn't using TrueCrypt.
On the first reboot for the update, the laptop goes to the PC restore screen. Thus far I have just been selecting "Continue to windows 8."
Full WindowsUpdate.log http://pastebin.com/hGmAW4Q1
Update: Turns out it was TrueCrypt! I decrypted the drive, installed Windows 8.1, and then re-encrypted the drive and it worked just fine.
Best Answer
You should decrypt the HDD before doing the update. TrueCrypt is a 3rd party encryption and during setup Windows doesn't know how to handle it.