CCC is a .NET application doing little more than changing registry entries. A faulty graphics card won't do sh***t to it.
You either have a faulty .NET install, a borked OS or just generic system instability due to faulty RAM, too much OC etc.
I suggest you run the usual stability tests. (Memtest86, Prime95, Furmark etc.)
CPU: AMD Phenom II X4 810 @ 3250MHz | RAM: Kingmax 2x2GB DDR2 800 @ 833MHz| MoBo: MSI K9A2 CF v1.0 (BIOS: 1.D)| GPU: Asus HD 6850 1024MB (DirectCu) @ 850/1150MHz | Display: L24FHD | PSU: PC Power & Cooling Silencer 750 Quad | OS: MS Windows 7 Pro x64
CPU: Pentium 4 Northwood S478 @ 3200MHz | RAM: 1,5GB DDR 400| MoBo: Gigabyte GA-8S661FXMP-RZ | GPU: ASUS Radeon X1650 Pro 256MB | Display: Dimarson 19" CRT | PSU: Noname 400W | OS: changing twice every week...