Why did the Stoics think the universe is a living, rational being that burns up and starts over?

Because they thought God is not outside the world but a body within it, immanent throughout the cosmos: a rational, fiery breath that structures all matter. In Stoic physics only bodies exist, because only bodies can act or be acted upon. That includes the soul, which is a body, and even wisdom. Beyond bodies they allowed only four "incorporeals": time, place, void and lekta, the "sayables".

The Stoics made God a corporeal entity, identical with the active principle, and characterised it as eternal reason (logos) or intelligent designing fire or breath (pneuma) that structures matter according to its plan. Active principle and passive matter together make up the world and everything in it. So the entire cosmos is a living thing: God stands to it as an animal's life force stands to the animal's body, enlivening, moving and directing it. Unlike the gods of Greek mythology, this God is orderly, rational and providential, and humans each possess a portion of the divine logos.

Fire also sets the rhythm of the world's history. The designing fire was likened to a seed containing the directions of everything that will develop, and the Stoics held that the cosmos cycles endlessly between periods of conflagration, in which all is fire, and periods of cosmic order like the world we know. That raises an odd question: will there be another you in the next cycle, or only someone exactly similar? Different ancient sources give different answers.

The picture is reconstructed. We have no complete work by Zeno, Cleanthes or Chrysippus, so our view of early Stoic physics rests on incomplete evidence.