"Outlook is closing" in Notification Tray - Can't reopen without killing the process

Solution 1:

I had the same issue. Without disabling the add-ons, the following steps worked for me:

1) Hit Control-Alt-Delete
2) Click Task Manager
3) Go to 'Users' Tab
4) Under User name (usually an email address), expand/collapse all the programs. 
5) Search for Outlook.exe and 'end' the process by using Left click of the mouse.

This will kill the process altogether and you should be able to restart Outlook with a click.

Solution 2:

This issue is mostly caused by add-ins. Try to run Outlook in safe mode first: outlook.exe /safe. If this mode allows it to exit properly, then disable your add-ins one by one to find the falty one. After that contact the add-in's developer.