This can only happen in one of two ways:
In most cases this is caused by a Blackberry as it defaults to removing the message from the server, but if you don't have one, you'll have to check your devices the hard way.
To troubleshoot this, we usually recommend turning off all devices that are configured to receive email, then send a test email from an external email address (like Gmail or Hotmail). Turn on one device, make sure you've received the message and all is well, wait 30 minutes, then turn on each device in sequence until you find the one that gets the message then wipes it from the server.
Once you've found the culprit, you can do one of two things to fix the problem: