Sounds like you are downloading your mail to a pst on another computer. Do you have more than one computer on which you have set up Outlook? This is the behavior I typically see when this happens. The email “pops in” for a second and then just “disappears”. Check your other computer/s and see if you have mail downloading to a pst on one of them. You will have to move all that mail back into your exchange account.
Another option is that there are rules setup that move all incoming messages to either another folder in the mailbox or forward and delete the message. I’ve seen a situation after a mailbox migration where mail got lost inside the mailbox because a rule in the mailbox moved the messages to a non-existing folder. The messages disappeared from the inbox and could not be found anymore. Very strange but true.