My iPhone is also deleting emails on its own. In my case, the emails seem to be disappearing from folders that I moved them to on my iPhone.
This weekend I know that I moved a number of emails from the InBox to several of my folders on my iPhone, it seemed to move fine. I could see the email in those folders on my iPhone. Here's the odd part: when I opened the folders the next day, and it connected and updated, I saw the emails disappear right in front of my eyes, and the emails were lost.
It was almost like under some circumstances the folder connections are automatically overwriting the iPhone's contents with the contents from Yahoo's server rather than seeing that new contents moved into the folder on the iPhone and synching them back with the server.
I just tried it, and of course, it didn't overwrite my email. On the other hand, immediately after moving the messages on the iPhone, they were not visible in the folder. The messages were only visible upon reconnecting in the folder.
Very strange...