Asking if the theoi can die is like asking if time can end.
After-all, Kronos is a god. ; )
Statue of Kronos, Titan God of Time & Father of Olympians
I follow the ancient theory that time is cyclical. Pythagoras described history as one Great Year in which the historical cycle comes to an end and the sun, moon, and all other planets return to their original positions. The very same people return to earth and all that had happened will happen again.
It was only later that St. Augustine promoted the Jewish and early Christian theory that time is linear, following an irreversible process, with a unique beginning and ending, and a god that existed before time.
Some things to chew on:
The cyclical nature of time is appropriately in line with the theory that the Big Bang repeats itself. The universe (which we could understand as Chaos or “the Void”) expands, but like a rubber band, eventually pulls back upon itself in an implosion before exploding again.
Time might appear linear to us who perceive our small length of the great circle as a perfectly straight line with a single beginning and ending.
If time is cyclical, then the theoi don’t “die” so much as transform (like Helios into Apollon and Selene into Artemis) through the process and, at the end, revert to the beginning. That is, brought back to Chaos (or “the Void”). Eventually, the Earth (Gaea) is “born” from Chaos, and the theoi are born from Her. And the rest, as they say, is Hesiod.