Two ideas, one's a "duh" and the other you won't like at all.
First idea is that you have a desktop or other peripheral checking your account and deleting the messages from the server via POP. I have two Yahoo accounts and used Zimbra for ages until recently, tried using the native OS X Mail app and had that same "duh" moment when a few messages in one account "disappeared"; I switched to using webmail and the messages "mysteriously" stopped disappearing. Duh. Until a couple of weeks ago...
Here's the one you won't like. A couple of weeks ago, I got an email very early in the morning from one of my employees, saying that the link in an email I sent to him didn't work. After a few seconds of wondering, then a bit of panic set in when I got a second email, this one from a client, to the same effect. I logged into one of my two Yahoo accounts, and saw two more emails indicating "undeliverable" back from two more clients, with several other of my contacts in that account being shown as on a distribution list. Then, the two emails in my inbox "disappeared". My Yahoo account had been hacked, someone had siphoned off my contacts list and was sending email spam - but from a remote email client - the "sent" messages weren't in my account's sent outbox. Sh*t, I thought (without the asterisk) and got to a bit of a web search - I found the Yahoo page that seemed to be set up for just this purpose, and did what it recommended -
changed my password - and then sent out a email to everyone in that account with a mea culpa. Evidently, several messages had been sent out, a few emails had been deleted, and I don't know if a local copy of my contacts had been swiped.
Yahoo! Account Help | - SLN2068 - Spam is being sent to my contacts from my Yahoo! account
Since the password change, no more damage has been done, no more emails have randomly "disappeared", and I haven't been "spoofed". Had I not seen the messages being deleted before my eyes while in my webmail account and the rejection messages (complete with headers) for myself I may not have believed anyone else telling me it would happen. I made the mistake of trusting Yahoo, it turns out what happened to me isn't a unique experience, a few of my friends have had it happen to them too.
It wouldn't hurt you to change your password, and I hope for your sake it's something else? Like, a "duh" moment?