We've observed brains shut down - not consciousness. We have no reason to believe it can be created or destroyed. Simple.
We have in fact observed concoiusness shutting down. This is simple as well. All one need do is watch someone die and then try to carry on a conversation with them. Attempt to get any sort of response other than their body moving about as you move it. That's about the level of awareness you can discern. We have in fact observed that as brain activity shuts down, consciousness too shuts down. We do this by merely asking the subject questions until they stop responding altogether. By noting the very strong corrolation between response and brain activity, we can easily come to the conclusion that brains make people concious.
This is conclusive because, simply put, there is NO compelling evidence to suggest that concoiusness is anything else or that it continues to exist. You are supposing what you WANT but you lack any evidence at all. You are not taking the default skeptical position.
You just state "we have no reason to believe it can be created or destroyed" but we DO have every reason to believe that is the case. We watch the corrolating behavior all the time.
Listen, it is very simple. I keep having to resort to analogy because you refuse to see this evidence for what it is. What sort of evidence do you require? Do you deny that turning a light switch results in the light turning on because that is merely corrolation? Does the repeated corrolation not suffice as proper evidence? How many times must you flip a light switch and watch it's direct response before you can conclude that the switch does in fact produce that output?
We need only observe the results of concoiusness to state that conciousness is there. Do you need to touch, taste, feel, hear, see, and "6th sense" a light bulb to identify it? Let me go further, how can you observe, directly, the light bulb's "reality as a light bulb" just by looking at it or feeling it? You aren't actually EXPERIENCING the bulbitude (not that it is a possiblity) so all you can say when you turn it off is that the light coming from it is no longer being made, but you haven't actually BEEN the bulb to EXPERIENCe it's "not on" status, have you?
Do you believe they have any degree of consciousness at all?
About as much as any single celled orgamism. Possibly less. I am unable to quantify it, but it is at least not aware of it's own existance at all.
What's the correct level of complexity? Why doesn't less complexity produce consciousness?
Not the correct LEVEL of complexity. The correct CONFIGURATION of complexity. Again, you confuse SIZE with STRUCTURE.
The correct STRUCTURE, is unknown right now. Programmers are still working on that one

. They are starting to replicate certain facets of conciousness though.
However, your question is silly as it can apply to a program as well. A computer has to be made, in the end, of smaller parts, but a RAM block on it's own does not a running program make. It takes all of it TOGETHER to make a computer.
Since, with careful observation, said complexity can actually be shown to be made up of lots of less complex systems how do they work together to generate consciousness?
Like I just said, you could ask the same question of a computer. However, it is stupid. You need the WHOLE THING. You can't call just the RAM alone "the currently running program".
When have you observed consciousness, as opposed to neurons, being destroyed exactly?
_
HypnoPsi
Well, why not examine the breakdown of a human being going through some brain decaying disease? You can observe it for yourself first hand, though to be honest I hope it doesn't take something as nerve shattering as that to wake you up to this.