A closed window is not a closed Outlook: the process stays until every add-in releases it and every data file finishes its shutdown write. Something in your setup holds a reference past the close. The usual suspects, most common first:
1
Add-ins that never let go. Test by running a session in outlook.exe /safe, work normally, close and watch Task Manager. A clean exit in safe mode convicts an add-in, then File, Options, Add-ins and disable the recently added or ancient ones first, sync utilities and PDF integrations lead this category.
2
Hidden windows still open. A reminder popup, a stray message draft or an open properties dialog behind other windows keeps the process alive legitimately. Check the taskbar and Alt+Tab before closing, and close via File, Exit rather than the X, which asks Outlook to shut down rather than just hiding the window.
3
Oversized or damaged data files taking forever on the shutdown write. If the process always lingers proportionally to your PST sizes, compact them: Account Settings, Data Files, Settings, Compact Now, and run SCANPST over any file that has crashed recently.
4
Third party mail scanning in the antivirus holding the process while it finishes inspecting. Temporarily disable the AV's mail or Outlook integration module and compare exit behaviour, that comparison convicts or clears it in one test.
While diagnosing, resist Task Manager's End Task except as a last resort: killing Outlook mid shutdown write is precisely how PSTs corrupt, which then makes the slow exit worse on the next cycle. The safe mode comparison in step one finds the culprit in the great majority of cases.