It's also about time we had a Canon 1.4x and 2.0x extender that retained AF past f5.6/8.0 - I'm sure it's a marketing ploy rather than technical - or at least extend the f8.0 AF capability to the recent batch of midrange cameras - 6D & 70D with a disclaimer
It's not the extender which stops AF from functioning. It's not the lens. It's the combination of the two which creates the resulting maximum aperture, and that's either inside or outside of the range of the AF system built into the body.
No-one creates a 1.4x converter which doesn't result in a focal length 1.4x longer and an aperture one whole stop slower.
And similarly speaking, no-one makes a 2x converter which doesn't result a focal length 2x longer and two whole stops slower than the native lens.
The only workaround to keep AF working (and without bodges) is to make sure you've got the maximum aperture of the combined lens/TC within the AF limits of the body.
Phase detect AF works by comparing the two phases (halves/sides) of the lens when looking at an object - exactly like a split prism focus screen. If the aperture is too small, those off angles required aren't supplied by the lens, so the split prism goes black (or the AF module gets no light). It's as simple as that.
There is usually a small margin in there, so there will be a software limit slightly before the hardware limit; this is simply the manufacturers way of producing a product where people don't get bad AF experiences.
For instance, the old taping the contacts trick to fool the max aperture, or use a 2x and a 1.4x to get incorrect reporting (or even a zoom which reaches f6.3 at the long end) all trick the AF system into thinking it's got a lens within its limits, so AF functions.
I've tried a 70-200/2.8 with a 2x and 1.4x on a 40D - f8 lens on a body which should only AF up to f5.6 - AF operated, but it hunted all over the place without locking on. I did occasionally manage to get something out of it by manually focusing and then letting AF take over once I'd done all the hard work, but even then it had about a 90% failure rate.