In this question you talk about the fact that 500-1000 miles variation of the distance between Earth and Sun would not cause catastrophic temperature variations. What distances would? How much variation would be needed to extinguish life as we know it?
That's a pretty tough question to answer, because the effect of orbital variations on climate is not very well understood. We know that small changes in the eccentricity of Earth's orbit (that's a measure of how much the Earth's orbit is an oval, rather than a circle) can cause ice ages, but how big a change would it take to cause a permanent ice age, or to raise the Earth's temperature enough to cause a runaway greenhouse effect, like we see on Venus?
The habitable zone is the region around a star in which water will be liquid at the surface of a planet. The habitable zone around the Sun (depending on how you calculate it) is about 0.95 AU to 1.69 AU, though these numbers may vary in time due to the size/activity of the Sun. An AU is the Earth's average distance from the Sun, 93 million miles, so the Earth's orbit could decrease by 4,500,000 miles or increase by 34,000,000 miles and still be in the habitable zone.
A large change in the Earth's orbit would have big consequences for our climate, and would lead to the extinction of many species. However, to destroy all life on Earth the orbit would have to change by at least hundreds of thousands of miles, though even that may not be enough!
This was last updated on June 27, 2015.