page-break-after avoid not working

I have this set up in CSS. All headings are display:block

I simply cannot get page-break-after:avoid working.

I have H1 with a break before. Fine.
I also have H2 with a break before (necessary for the content type).

But I want H3... to NOT break after. But I still keep getting H3, H4, etc. at the bottom of the page. I want them to appear on the same page as the text.

Even the Amazon docs says this should work. But I tried it with a minimal test file and it still doesn't.

Any ideas?

Thanks, chaps.