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When I try to open Outlook, it closes on its own within seconds. However,
when in Safe Mode, it opens and stays open.
Well, if "safe mode" meant that you started Outlook in its safe mode
(and are not referring to Windows' safe mode) then you did not load any
add-ons when Outlook started. When Outlook loads, it also loads all the
add-ons that you have installed into Outlook. If one of them fails to
load then Outlook fails to load. Similarly, when Outlook exits, it must
first unload all the add-ons, so if an add-on refuses to unload then
Outlook cannot unload. Outlook's safe mode does not load any add-ons.
So your problem is with an add-on.
You can disable the add-ons and then reenable them one at a time to see
when the problem reappears for what add-on.