CarrionCrow: First thought - looking at each organism, whether human or not, being a small thread, interconnected and woven into the larger, overall thread of energy that keeps everything going.
A person's thread frays, they die. No coming back. For gods, possibly strands that connect them to points that mortal races can't.
How did the gods go away? Most of their threads were cut, maybe to the point that they couldn't actively interact with the mortal world, but still bound sufficiently to still exist in some state that no living mortal could.
How does a demi-god work? Well, you get two mortals together, they reproduce, you get a new mortal thread.
A god and a mortal reproduce, you get a reinforced thread. Stronger the thread, the closer to divinity you are.
The tricky part would be how exactly the gods went away and what they have to do to come back.
First thought - someone managed to find a way to unbind the threads and did so. Why they did it? Who knows. Maybe the gods were complacent, omnipotent assholes that needed a good comeuppance so they'd stop abusing the world with their power. Or something. That's up to you to decide.
But anyway, as for how the gods come back? Well, they might have to sacrifice part of their own essence, losing connection with some things and redirecting the threads to essentially reattach themselves to the world.
Or maybe, mournful followers develop a way to ritually sacrifice themselves in order to give over their threads to their god, allowing the god to rebind themselves at the cost of their own existences.
Ooo, I like this. Actually fits really well with one of my systems of magic (which is based around a tapestry of Life called the Weave which is basically all the possible pasts, presents and futures woven together. So powerful mages can change what happens by affecting the Weave while Seers can see the future and probabilities etc.) I can't remember if that was the system I was going to use in this world or not, but it fits quite well anyway so I might just tweak it about until I like it.