I know I’m not breaking any news here, but I happened to have some time yesterday and I decided to take a look at the issue of Outlook now quitting when it’s supposed to quit. Basically you exit the program (either properly or by going to File > Exit), but it remains running and you can see OUTLOOK.EXE in Task Manager. End Process does the job but preferably the thing should just exit on its own.
If you scroogle the Web for this you’ll see that there are several reasons and solutions (or workarounds). What worked for me was disabling the offending plug-in/add-on (Tools > Options > Other > Advanced Options > Add-In Manager|COM Add-Ins). I don’t know which one it was but I disabled few non-essential ones and now the thing disappears from Task Manager within five seconds.