There is a very specific reason why cameras cannot focus beyond f/5.6 most of the time (or f/8 on top end professional grade cameras). It should be noted that the camera's image sensor, which is what ISO affects, does not handle AF in a DSLR-type camera like the 600D. A dedicated AF unit with its own special sensor that is housed underneath the half-silvered reflex mirror is actually responsible for handling autofocus.
The first issue is comparing your eyesight to the AF sensor (or even the image sensor) in a camera. The human eye is a truly amazing biological device. As an imaging device, while in terms of resolution it may be somewhat mediocre by digital sensor standards of today, in every other respect it is vastly superior to anything manmade. Our eyesight is truly dynamic, and adapts very quickly to relatively small changes in light...such as when you put the viewfinder of a DSLR up to your eye. The light-sensing mechanics of your eye and brain immediately react to the drop in luminence, widen the pupil (iris), increase the sensitivity of the cones and rods in your retina, and probably adjusts how your brain perceives the dimmer light as well. That all happens in a the blink of an eye.
In contrast, digital sensors are not really dynamic in that sense. The image sensor on your camera has a fixed range of luminence that it can record, anywhere from zero to its maximum saturation point...called its dynamic range. That range does not change, however you can record images of any contrast range so long as they fall within the fixed dynamic range of the sensor. (The human eye has both a dynamic adaptation to light as well as a non-fixed range of sensitivity to luminance...in normal daylight for example, the human eye cannot generally see deep into shadows...however if you actually move to the shadows and stay there for a while, your eyes will adjust to the dimmer light over time and the sensitivity range of your eyes will be different than when you are in daylight.)
The AF unit of a DSLR is also a digital sensor...and therefor it is bound by the same general rules as a normal image sensor. Unlike an imaging sensor, however, AF sensors do not have the ability to amplify according to ISO and therefor compensate for a narrower aperture...they work on a fixed sensitivity, and thus have to work with less and less light the narrower the aperture. AF sensors are designed to be highly sensitive, as the AF unit the sensor resides in is responsible for splitting the very little light that is directed down toward the AF unit (which is a fairly small fraction of all the light coming down the lens in general...barely 60% of half the total light at most, as half is reflected up into the viewfinder, and the AF unit mirror under the main reflex mirror is usually around 40-60% the size of the main reflex mirror). A special lens above the AF sensor is responsible for further splitting light...into as many AF points as your camera has (9, in the case of the 600D), and each of those bundles of light are split onece more to support phase-shift detection AF. The AF sensor itself is composed of split rows of CMOS "pixels", each row of which senses light from one of the 18 split beams of light projected by the AF units special lens. By now, it should be readily apparent how little light an AF sensor must work with.
This limitation generally does not affect normal every-day DSLR use with Canon cameras like the 600D. Canon cameras perform AF while the lens is wide open (at maximum aperture). So long as your lens is an f/5.6 lens or faster, AF should work regardless of what aperture you have actually selected. You could select f/22, and the camera would perform AF before stopping the aperture down and opening the shutter to expose a photograph. The only time the sensitivity limitations of an AF sensor would be a problem is when you are working with an aperture smaller than f/5.6 (usually, f/8). This can occur when you attach a teleconverter, either 1.4x or 2x, to a lens that does not have a wide enough starting aperture. You can attach a 1.4x TC to an f/4 lens and still AF, but not an f/5.6 or slower lens. You can attach a 2x TC to an f/2.8 lens and still AF, but not to an f/3.5 or slower lens. If you are lucky enough to be using one of Canon's 1-series bodies (except the 1D X), you will have the ability to AF at f/8 with the center AF point, however even that has its limitations...AF tends to be fairly slow to ensure accuracy with such little light.
Because AF sensors have to work with such low light, this also limits their capabilities in diminishing light. If you are taking a photograph that requires ISO 12800 on a 600D, then there is VERY little light to work with...probably too little for the AF sensor to do what it needs to do on common lenses. If your using the most common kit lens that came with the camera, your maximum aperture range is f/3.5 at 18mm and f/5.6 at 55mm. Neither of those apertures are wide enough to allow AF in very low light. You would need to use at least an f/2.8 lens, but probably an f/1.8 or f/1.4 lens to really get decent AF performance in light so low that you needed to use ISO 12800. Canon makes several 50mm lenses with very wide apertures. There are also several professional-grade zoom lenses that have f/2.8 maximum apertures. You would need one of those lenses to AF in the dark.