Question about chronic insomnia due to anxiety

How come people with chronic, anxiety insomnia stay alive for decades? Does the basic biological survival mechanism always, in the end, make sure that the person gets just enough sleep in order to stay alive?

I was wondering this especially concerning chronic insomnia caused by anxiety. I understand that this problem is caused by a vicious circle where a person fears they won't fall asleep and because of that they won't. That's what they say. But surely anxiety isn't stronger than the biological survival mechanism? So despite a very strong anxiety, basic biology will always make sure the person sleeps at some point, no matter how anxious they are, right? If it weren't so, we would have a lot of people die from anxiety insomnia all the time.