I can not reproduce in FF 6.0.1; however, perhaps you can get around this with
background-color: transparent;
in the heading # or in white if you do not want it to be viewed.
This should still give the fix you mentioned, while leaving an empty div.
Update:
Well thanks for the screenshot, I still can’t reproduce, this time with ff 6.0.2 - I looked around after I noticed that I can reproduce a similar problem at different zoom levels.
A blog post explaining the scale-out error that includes this test page . I'm not sure if this is connected, it seems to be similar, but not the same, a zoom error will remove a fragment of the entire page, including the border # header-content.
As for your comments around transparency, you can use them and still provide a background image, doesn't this work for you?
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