I had this error message on 5th Dec 2016 and have managed to repair it myself, having tried using Microsoft's repair kits etc. It was scary, but here is what I did, cutting out the bits which simply got me nowhere.
I started on the MS support page
https://support.office.com/en-gb/article/Outlook-not-responding-stuck-at-Processing-stopped-working-freezes-or-hangs-5c313d04-64af-4441-82d2-44e5a43eee5a?ui=en-US&rs=en-GB&ad=GB
Having worked my way through the suggestions I arrived at Step 5 - Repair your Outlook data files.
This seemed logical as my 'hang' seemed to be being caused by Outlook having problems in downloading e-mail from my server. The link at step 5 takes you here
https://support.office.com/en-gb/article/Repair-Outlook-Data-Files-pst-and-ost-64842a0a-658a-4324-acc6-ef0a6e3567cd
Now, I didn't know if I was trying to repair a file - but if it was a .pst file, I am so unclear about what it could be and where it could be that I chose the option 'Re-create an offline Outlook Data File (.ost)'. When
taking the action suggested it looked simplest and least risky, but I was concerned when I reached the very last bullet point -
4. In the file explorer window, right-click the Exchange data file and then click
Delete. The next time you start Outlook, a new .ost file is created for the account.
My problem was that when a solution suggests that you delete a folder, what happens should the solution not work and you have a bigger problem to fix. And sure enough, having deleted the folder, and when I tried to re-start Outlook, the program wouldn't
even open! However, rather than panicking, I simply went to my 'Recycle Bin', found the deleted folder and re-instated it. Then, and without first being tempted to open Outlook and check if it was working again, I re-started Windows. When I opened Outlook,
voila!, it was working properly again.
Now, this may have worked for reasons only down to my PC configuration - I boot from a SSD - Drive C - but keep data etc on a standard HDD - Drive E. When I couldn't open Outlook, as mentioned above, it suggested a problem in reading files from my E drive,
which are the data folders, whereas the system program would be run from my C drive. I also run Office 2016 Professional on Windows 10. I'm a (retired) home user and my e-mail/ISP is BT.
If you want to give this a try, I wish you well. I understand why you may not trust to try this, and I did get seriously worried at one point myself, but basically I just followed the Microsoft actions to the point where it seemed to fail and I couldn't
open Outlook, restored the deleted folder and Bob's your uncle. I'm merely adding another potential action on to the MS fix.