I can speculate a little, but I think it is at least "informed" speculation based on some experimentation with the live preview code here.
This seems to be an idiosyncrasy with how MathJax is implemented on this site (and probably the other SE sites that use MathJax too). Essentially, only the last editor+preview pair that is created on a page will render the TeX that is typed into it. (Mostly - see comment.)
- When composing a new question, the main editor (where you type the question) and its preview are active on the page first, and they will render any TeX input.
- When you click the "Answer your own question" checkbox another editor+preview pair is created below it and hooked into MathJax. The new preview will render any TeX typed in this new editor.
- The first preview on the page will no longer render the TeX from its editor if you go back and change something.
This behavior occurs on question pages too (like this page you're on now, for instance):
- Type some TeX into the "Your Answer" box at the bottom of a question page.
- Scroll up and click the "edit" link on an existing answer, so that a new editor+preview pair is created.
- Scroll down and type some more into the "Your Answer" box.
It seems to me that there is only one path through which an editor+preview pair can be hooked into MathJax, and when a new editor+preview pair uses the path the old pair is disconnected.
I've tested some ways to get multiple editor+preview pairs running at once using the tech available to Math SE. The result, using a minor modification of SE's
mathjax-editing.js file, can be seen here: Pagedown + MathJax example.