Perhaps Apple is assuming we all have a Time Machine drive hooked up. Whatever the reason, they have not seen fit to provide a straightforward way to backup Mail.app Notes.
There are two easy solutions, and while they will not update or sync in any way, at least you can recover your notes if you inadvertently lose them all.
If you have just a few notes, the first and simplest is method to make a text clipping.
- Select all of the text in your note.
- Click and drag the selected text onto the desktop or your backup folder.
The second involves digging around in the Finder to find where the note files are stored. I found my Mobile Me notes in:
~/Library/Mail/Mac-*username*/Notes.imapmbox
Substitute your own account's shortname for *username*. I then copied the Notes.imapmbox file into my backup folder.
[crarko adds: I tested this, and it works as described. I do have a Time Machine drive hooked up so sometimes it's too easy to forget those who don't.]

