You can "save" one draft answer at a time.

If you feel that you need to keep multiple drafts at a time, you can use your email account (supposedly GMail, but anything works really). Type the answer on the page (to see it compiles with the MathJax and whatnot), then copy it to a draft email whose title is the question name/link/whatever you feel like. Save the drafts and return to them easily.

If your MathJax/LaTeX abilities are sufficient then you don't really need to compile the answers, and you can type them directly into an email draft.