I’m having the same problem, and the [embed] shortcode doesn’t help, it just creates a text link to the video.
If I edit the html code and then never, ever touch the page again, everything is fine. I can paste in Youtube’s <iframe> code, update, and leave the editor, and the video is embedded correctly. However, the minute I go back in to edit that page, WordPress kills the <iframe> code and suddenly the video is gone.
I’ve read on other threads that the two “solutions” are to hack the WordPress Code, or never use the visual editor. This seems a bit pointless, WordPress is supposed to be easy to use, and it’d be nice if it could handle something as common as embedding video. If I wanted to use raw HTML or modify source code, I wouldn’t be using WordPress in the first place. In addition, there are other people working on this site who have absolutely no html experience, so when someone edits in visual mode and WordPress discards all the embeds, the page is broken.
