After one of my recent Windows Updates, Microsoft Outlook has stopped syncing the emails and was not downloading any new ones. While my other accounts were syncing, one Hotmail email account had stopped syncing. If you face such a problem this is what you could repair your Outlook account. That helped me.
Outlook not syncing
Open Microsoft Outlook and click on the File tab. Now under Info, click on Account Settings and open the settings for the affected account.
When the Account Settings open, select the email account which is not syncing and then click on the Repair button.
The Repair Account box will open. Check your settings and fields and then click on Next.
Repair Outlook Account
Outlook will start the process to repair the Outlook account.
It will enable network connection, search for the email account settings and log on to the server to confirm that all is fine.
Once the process is completed, you may want to also click on the Change Account link, check the settings and then click on Next.
Outlook will test the account settings and give you a message if all is well.
Click Close and you will see this box. Click on Finish.
Restart your Outlook and see if this has helped you. If need me sync manually by clicking on the Send/Receive button, the first time.
Hope it helps you!