It's a little known "feature" of Outlook: clicking on the X in the upper right to close the app doesn't really close it; the process continues, but the GUI (aka window, aka front end) is closed. Use "Exit" from the File pull-down menu to do an actual exit.
Try it both ways a few times and observe its behavior in Task Manager. If Outlook doesn't drop out of the processes image name list, then something else is running that needs Outlook to be an active process even if the GUI is closed. For example, if you have alerts set up in tasks or calendar. Or a third party add-in, misbehaving or not.
To check on your ad-ins, in Outlook navigate to:
Tools > Options > Other > Advanced Options > Add-in Manager
Un-check stuff one at a time to find a possible culprit.
If you know for sure you have nothing hooked for Outlook to act upon, terminate the Outlook/Exchange provider in Avast! and see if that resolves your Outlook process issue.
If there is no reason for Outlook to be active when the GUI is closed, then there is indeed a problem that needs to be addressed. If all else fails, an unistall/re-install might be needed. Though tedious, ending the process in Task Manager is an effective work-around.
Good luck.
