The OP is terribly confused.
"What happens to our consciousness when we die?"
The question makes no sense. The irreversible disruption of metabolic chemistry that for reasons of convenience we all call death implies also the irreversible destruction of consciousness. Asking what happens to consciousness when we die is like asking what happens to a bird flying formation when they land.
[N]euronal firing [only represents] the preconditions that seem to produce consciousness that can/do communicate/demonstrate its consciousness to us.
Any other factors would be irrelevant. With no self-awareness, there's no consciousness worth speaking of.
In short: Physical destruction of the brain entails destruction of consciousness because your consciousness resides entirely and solely in your brain. If the brain tissue gets too damaged (most commonly from lack of oxygen), it dies, and you with it. There is not, and cannot be, any afterlife.
I've read a fair amount on Less Wrong and can't recall much said about the plausibility of some sort of afterlife. What do you guys think about it? Is there some sort of consensus?
Here's my take:
Edit: People in the comments have just taken it as a given that consciousness resides solely in the brain without explaining why they think this. My point in this post is that I don't see why we have reason to reject the 3 possibilities above. If you reject the idea that consciousness could reside outside of the brain, please explain why.