In the field of astrobiology it's become received wisdom that complex-celled (eukaryotic), multi-cellular life is not as adaptable or as tough as microbial life. As a result, when scientists discuss the planetary requirements for life, they typically divide environments into those that are somehow 'stable' enough for complex life, versus those that might support microbes but not much else.
Long-term climate stability is one factor that is thought to matter a lot, and especially climate linked to the variations in a planet's rotational and orbital configuration. Here on Earth we're subject to the Milankovitch Cycles, a set of interlinked and overlapping periodic variations in properties such as orbital ellipticity, axial tilt, and axial precession (where the Earth's axis points at given times in its orbit). These cycles exist because of the gravitational interactions of the Earth and all the other objects in the solar system - like the Moon, Jupiter, Saturn, and so on.
The net result is that for at least the past few hundred thousand years Earth's climate state has been driven (in a major part) by these configuration shifts that change how solar radiation hits the planet. For example, the geological record of ice ages shows good correlation with the Milankovitch Cycles.
However, compared to the spin-orbit variations that could happen to a rocky planet, the Earth seems to suffer only a mild case of these perturbations. For example, Earth's axial tilt only shifts back and forth by a couple of degrees over time. It's long been pointed out that it's the specific Earth-Moon configuration that helps prevent the Earth's spin axis from undergoing much more extreme variations. By comparison, the planet Mars sees its polar axis vary by tens of degrees over just a few tens of thousands of years. And many distant, rocky exoplanets could also suffer these kinds of instabilities.
The idea that Earth's mid- to long-term climate variation is 'just-right' for complex life has sometimes been extended to argue for an anthropic selection effect, and used to support the idea that complex life may have very few opportunities to establish itself across the universe.
But is the root assumption about complex life needing nice conditions at all reasonable?
It's not clear to me that it is. While it's certainly true that there are environments on Earth where only microbial life survives (scalding ponds at Yellowstone, or deep rocky cracks in the Earth's crust), complex multicellular life is also pretty well embedded across very different conditions.
And when it comes to resilience to major environmental shifts, the history of the planet suggests that complex life does ok. Consider the largest recent mass extinction, the fearsome Permian-Triassic event some 252 million years ago. At this time about 70% of terrestrial vertebrates, and up to 96% of marine species disappeared. This was a doozy of an extinction. Yet, complex life as a whole did not go away. It did of course change, with new forms expanding into the niches left from the extinction, but it absolutely did not vanish.
Of course, it could be argued that sudden extinction events are different than a constantly changing environment that might not allow complex life to happen in the first place. But I have a hard time seeing that we have any quantitative evidence to support this hypothesis - it just seems that we've adopted the idea that complex life doesn't happen in very changeable environments, end of story.
Perhaps the issue is that we focus on specific groups of complex life. It is certainly true that something like climate change can wreak havoc on established species - the plight of today's arctic organisms is a good example of that. Ecological science can pinpoint many, many examples of how even seemingly innocuous changes can wipe out unique life-forms. But does that mean we can extend the idea to complex life as a whole?
I'm not sure we can. If we relinquish the need to sustain specific models of complex organisms (even the great collectives of vertebrates and invertebrates on Earth) then it seems much more likely that some form of complex multicellular life will find a way through the hurdles of selection.
In that case, worrying about the 'just right' state of Earth as we hunt for analog worlds around other stars, may not be necessary or desirable.