Outlook inbox not automatically updating
Amongst others, the update makes sure that IMAP accounts will not repeatedly completely resynch folders, will not create duplicates of default folders, will more reliably map the special server folders and make it less likely that folders will get marked as “This computer only”.
However, it is now also more important than ever to correctly set the Root Folder Path for your mailbox when your IMAP server requires it.
Thus, your Inbox will appear to have a set of missing emails. The problem is that IOS Apple Mail hasn't "fetched" those gap emails yet and therefore is not showing them in your other email clients on the face of the planet (including Apple OSX Mail) fetch from your mail server by latest arrivals first instead of most recently copied or moved.
Or fetch them all, which avoids the problem as well.1.
You can in fact access the more recent items (via your web mail or even an alternate email app or email client.) The Mail app is actually grabbing the wrong subset of your Inbox email which causes some email to appear to be missing.
It has come to our attention that many Outlook 2013 and Office 365 users are having issues within synchronizing IMAP folders recently.
This appears to be happening across all hosts due to a recent update that Microsoft has pushed out to all of its users.
If it works by disabling Cache Exchange Mode, then recreate the rule. After doing all this, you can re-enable the Cache Exchange Mode.
It looks like the recent updates for Outlook completely broke my IMAP account in Outlook 2013.
Keep scrolling down passed the bottom of your Inbox view to force the app to load more mail.