I've had type 1 diabetes for 9 years. In the first 3-4 years my liver continued to produce glucagon. I experienced highs resulting from the down syndrome over night. But after that it just stopped.
Now I automatically wake up if my blood sugar is below a certain threshold. It's a survival instinct. Sometimes though it gets very scary. I can't scream, know that I need to get up and eat something, but I just can't.
The downside is that I am very paranoid. I wake up at least once a week at night (around 3 am) and check my blood sugar levels. Even though they are usually in the expected range, I still get that feeling of 'being low'. If I don't act on it, I might die.