The important message that you were expecting did not show in your Outlook Mail. You may have received the email on your phone, but cannot see it on your desktop. What could be the reason for this glitch? Mostly, it happens because of a weak internet connection.
The email delivery issue can also happen due to a heavy inbox. Outlook Mail has a storage limit that shouldn’t be exceeded, or else you won’t receive any new messages in the future.
New Outlook users may turn on the “Work Offline” mode, which can prevent messages from being delivered. Outlook stops syncing with its web server, and they may wonder why they are not getting any messages. The email remains in the local OST file and will not sync with the server until the “Work Offline” mode is disabled.
Try these practical troubleshooting solutions that may help in resolving the Outlook not receiving emails in Office 365:
Open Outlook on your PC.
Select the Send/Receive tab.
Click on the Work Offline option.
You will see the Connected to Microsoft Exchange option at the bottom of the status bar of Outlook.
On your computer, open Outlook Mial.
Click on File.
Select Info and review the information under Mailbox Settings.
Check the folder size under Properties.
If the storage is full, delete unnecessary emails.
Recreate Outlook Profile
Click Windows Start.
Go to Control Panel and switch to Large icons view.
Select Mail to open Mail Setup.
Click Show Profiles, then select Add.
Enter a profile name and click OK.
Follow the Add Account wizard to set up your email.
Select “Always use this profile” to set your new profile as the default one.
Source:- Fix for Outlook Not Receiving Emails in Office 365