how do I stop html tag stripping

I really like fckeditor, but I'm having an issue where when I paste html into the source area and then apply it. The code disappears. In a module that already had some html in it. I pasted additional code in the middle and each time I did this process the html I pasted and the tag immediately above it disappeared. Eventually, all html was gone and anything new I paste just disappears when I Apply.

I've tried, switching back to non-source mode. It appears the stripping happens at this point.
If I have "fullpage" editing on, the default "page" tags do not disappear, but everything I insert between them does. If I put visible content, like an unordered list. That stays, but the divs disappear around it. I tried turning off "source formatting" and some other options. I'm using Chrome mostly, but did try in IE briefly, that appeared to leave the source html in, but as text rather than html code..

I've looked through the forms for a while and can't find an answer. What am I missing.