When I have Microsoft Outlook running on my computer, exchange emails are self deleting on my Samsung Galaxy S III.
I can see the incoming email on my Galaxy S III, but it goes as soon as Outlook downloads the same email.
Why is this?
This problem is due to your email server setup. Server is setup to delete mails from the server once they are downloaded to your Outlook. Your Android Email client only shows mails that are on the server, hence you can't see mails once they are downloaded.
You may have an option where you can disable deleting downloaded mails, however my corporate mail server doesn't allow me to do this and always deletes downloaded mails, so I'm not sure about this.