Recently I had an issue with my Exchange Online mailbox: there was almost every second a log generated within the Sync Issue folder, which contains synchronization error messages.
The log generated were saying
“Your server administrator has limited the number of items you can open simultaneously. Try closing messages you have opened or removing attachments and images from unsent messages you are composing."
Off course, no configuration changes were done.
The synchronization between the mailbox and Outlook client was deferred: all mails were not synchronized but some continue to get received by Outlook while sent mail were sent but not synchronized with Outlook cache.
To solve this issue, just close all application using Outlook cache (Outlook client, Lync client), open Windows Explorer and navigate to the location of your Outlook cache (default: C:\<user profile>\AppData\Local\Microsoft\Outlook for a Windows 7/Windows 8 client) and delete the OST file.
Restart Outlook et voilà, no more synchronization logs.