My question is not about "how to focus in the low light" or "how to focus a camera". The question is why the camera is unable to auto-focus in low light with high f numbers? 

In these conditions, I can see and differentiate the objects through viewfinder so how come the camera can't do the same even at the higher ISOs? What fails in the auto-focus mechanism of camera in these conditions?

Further information: 
The camera is Canon 600D. Highest ISO tried was 12800. The scene was an outside view from my window in evening. I tried many times but each time the camera failed to auto-focus at higher f number. I tried even the highest ISO as mentioned but to no avail.