Woah, we got ourselves a smart guy over here!
Anyways, I know that the neck is where the brain connects with the rest of the body and blah blah blah... But based on what we've done in the story, with using the fact that oxygen acts as a catalyst to regenerate the body, I wasn't exactly sure how I could explain why the neck area (what does it even do? Does it kill the Titans? Or just stop their healing capabilities?) was so vitally important. I didn't count the brain stem idea, because I assumed that they would just regrow it...
You read the manga? Oh do please, tell me more (about it, so I have a better idea of what to do)
Sorry if the use of Memes seems a bit rude, I'm just trollin
OOC : At the nape of the neck is the brain stem. The brain stem is pretty much the main road for all nerves to travel up to the brain, and it was pretty much the first thing early humans developed to become "human".
Like with all animals, snapping the brain stem pretty much brings the animal to a halt, as the brain can't send in any signals, and the body can't receive the signals. Additionally, take a look at this poor boy : http://www.youtube.com/watch?v=wwpO0oW2GFA
Anyhow, you can see that the normal bodily functions can still be done without a brain, although your finer senses AKA seeing, hearing, smelling, tasting, get wiped off without them. You can feel, although the memory of feeling five seconds ago wouldn't matter. Titans can regenerate their heads, as well as their brains, but why not the brain stem?
Perhaps it's too complicated to regenerate? Maybe there would be a risk of rewiring the body the wrong way if the brain stem were to regenerate?