Why? Possibly Your inbox is full.
Internet connectivity issues.
Mail server settings were not configured properly.
Could be a number of reasons why.
Try deleting the account from the phone, then add it back. Be sure the log in credentials are correct.
Try the account on a different device. Do you receive on a different iPhone?
Try a different wifi and see if they sync.
Outlook had some issues a week ago. Check with Microsoft support.