Mail.app inbox becomes blank after a few minutes of use
Is your exchange environment hosted? Office 365 perhaps? 

My mailbox occasionally does exactly what you describe. This was a known issue in ML, I would expect a fix at some point, but for now here are the few steps that I take that fixes it for awhile.None of this seems to be a "permanent" fix, but should last a bit longer.


Select the folder in Mail that is missing items.
Select "Mailbox"
Select "Rebuild" from the bottom of the menu.


OR...

You can rebuild the Envelope-Index by throwing it away, it's located at ~/Library/Mail/V2/MailData/


Your Library folder is hidden by default. Select Finder (in the dock) > “Go to Folder” and then enter “~/Library.”
In ~/Library/Mail/V2/MailData, delete any file that begins with “Envelope Index,” such as Envelope Index or Envelope Index-shm.
Mail will rebuild the Envelope index when it is reopened. It will take a few minutes to rebuild the entire index.


If you're using Office 365, I've had more success by disabling the "Use Auto-Discover service" on those mail clients that are misbehaving.