Outlook 365 - Cached Exchange Mode
Cached Exchange Mode is a feature built into Outlook that can make working with large mailboxes easier, but may cause delays in email being sent/received or prevent shared calendars from synchronizing.
Step-by-step guide
Right Click the inbox name and select Data File Properties
Click Advanced
Now select the Advanced tab
Make sure Cached Exchange Mode is unchecked
Click OK, and OK to save the changes