NOW - is it the responsibility of the US to keep a civil war from occurring? Should American kids die, Americans be deprived of medical care, etc., to prop up a puppet government and prevent a civil war?

Yes. We broke it, we fix it. Or at least hold it together long enough for Iraqis to take over.
Civil war is certainly possible, though not inevitable.
Partitioning may or not work.
One thing is inevitable - we leave now, there will be civil war.

The US military is now aware the insurgency cannot be beaten. So, we're looking at a forever situation.

cannot be beaten? Perhaps. How about minimized? How about raising the Iraqi economy to such a degree that Iraqis dont want to fight against it? call me a dreamer....

Is that a reasonable expenditure of American lives? Treasure? And the US has given up on the idea of "democracy", and is now praying for stability.

Was that a reasonable expenditure? Perhaps, perhaps not.
IS it a reasonable expenditure? Yes, it is. We went in, something we cannot undo. We have to deal with reality.
Given up on democracy? Sez who?
Praying for stability? well yes, that and 150000 US uniforms.