When using Exchange, ActiveSync or Office 365 Outlook defaults to only downloading the last 12 months of emails to your PC.
If you are exporting your mailbox you will want to download everything beforehand.
Warning: If you have a lot of emails on the server then this can take some time!
- Open Outlook and click on the File menu at the top left.
- Select your Exchange account and click on Account Settings
- From the Account Settings window make sure your Exchange account is selected and click on Change
- Move the Offline Settings slider all the way to the right so that it says All
- Click on Next and then restart Outlook
- When Outlook restarts it will begin to download all of your emails. Make sure it has finished before exporting.