If you want to have a repeatable pattern occuring every few thousand years I would suggest a biological reason rather than geological/astronomical. This way you can explain that the cycle is a part of a wider pattern in the ecosystem which lets you imagine more complex situations than just "boom! everything is destroyed! start to grow legs again, you stupid fish!" ;)
We are used to think that ecosystems are stable, but that's only because we have a very limited timeframe. Even though we know that there was a very different climate just twenty thousand years ago (and that now climate changes are even faster), our intuition tells us that summers and winters should be similar each year and nothing is really changing unless there is some kind of a catastrophic event. But that's only because our lifespan is 100 years tops. The ecosystem works on grander scale and doesn't need any meteorites or global volcano eruptions to go through different phases. It is also possible that there are intervals of short rapid changes followed by a long time of considerably more stable situation.
I would start with the assumption that the most complex life on the planet is amphibian or that all species which resemble mammals and birds are capable of spending their whole lives on water if ground is too hostile. When the conditions on ground improve, those species are able to quickly colonize the new ecological niche. But since a few thousand years is not enough for evolution, all those species will be dependent on water: so no complex animals in steppes, deserts, mountain plateaus, etc. That part of the world is left for a very different ecosystem, one composed of plants and animals which are smaller, simpler, but because of that they can multiply and spread very quickly when they reach certain "critical mass".
Think of it as a biological version of a nuclear bomb. We start with a very desolate place, a desert far from water. There are some species of plants and animals there, but they're rare and live in a fragile balance: plants grow, herbivores eat them, carnivores eat herbivores, less herbivores mean more place for plants to grow, but also carnivores starve, and this small cycle of small organisms (bugs? insects? miniature tentacle monsters from hell) repeats itself. But this is not really a balance. Every cycle the average population grows a little. And with bigger population, every cycle is a little bit more violent. At some point we reach the critical mass and everything goes boom - in the biological sense. The plants of this strange violent ecosystem spread rapidly around the globe. Herbivores follow, but eating not only the plants they know, but also one which survived in the waters and only recently started to colonize the shores. Carnivores follow, but hunting not only herbivores they know, but all the complex animal life which survived the last cataclysm living in the sea. The only way for the complex ecosystem to survive is to hide in the sea again: the miniature tentacle monsters (*) cannot be stopped. But when they finally eat everything in their way, they die of starvation. And since the cycle was so violent this time, only a very small number of the species form their ecosystem survive - somewhere far away from the shores, on the desert, starting a new small cycle within a bigger cycle which takes thousands of years.
*) I think it's too easy to think of them as a swarm of insects. I'd invite you to imagine something different.