I've inserted this code into each of the pages of the site I'm working (http://killerstuffandtonsofmoney.com/) on to add a facebook like button.

The code looks like this:

<div style="text-align: center;"><div id="fb-root"></div><script src="http://connect.facebook.net/en_US/all.js#xfbml=1"></script><fb:like href="http://killerstuffandtonsofmoney.com/" send="false" width="290" show_faces="false" colorscheme="dark" font="arial"></fb:like></div>

It works fine until I edit and update the page again to add content, etc.

Then the code changes to this:

<div style="text-align: center;">

<script src="http://connect.facebook.net/en_US/all.js#xfbml=1"></script>
</div>

And the facebook like button disappears.

Why is this?

sounds like the wordpress editor is messing you up. Are you using the visual or HTML editor? Try the HTML editor if you are not using it.

Yes, it is the editor. I paste in the code into the HTML editor. I switch over to the visual editor, to upload pictures, etc. However, if I go back to edit the page later, using just the visual editor, the code (which doesn't show up at all in the visual editor) gets changed. I can see this if I switch over to the HTML editor.

The thing is that once I hand this website over to my client, she'll be using ONLY the visual editor. She's very new to blogging/websites etc, so she will definitely not be using the HTML editor to add content.

This is a WordPress issue, not a theme issue. You might want to post or search about the issue at WordPress.org

okay thanks.

I like the Raw HTML Snippets plugin for stuff like that. It lets you create a shortcode for rendom html code which you can put in your post or page.