I'm working on a couple of projects – this site and another one – where I want to make my websites mobile friendly and use the many features of WordPress. I've been working with a combination WordPress and jQueryMobile to develop mobile friendly content.
I searched the Internet only to confirm that yes, indeed, this was what the WordPress team intended, and no, they did not see it as a "bug", rather it was a "feature". Uggg.
I searched for solutions and downloaded many different plug-ins that reported to solve this problem (HTML Editor Reloaded, PureHTML, Text Control, TinyMCE Advanced). Unfortunately, none of these solved the problem and many of them didn't seem to work at all.
Eventually, I called in my trusty IT support (my loving husband) who found a plugin the works (mostly). He found CKEditor for WordPress, which appears to solve my problem. I'm now able to edit in either visual or HTML mode and the HTML markup that I place is not deleted. There is a small issue with it adding a blank paragraph whenever I use visual mode, but for now that is workable.
So, if you plan to use both Visual and HTML mode for editing, and you don't want WordPress to decide what HTML to keep, consider loading the CKEditor plugin.