Windows IT Pro details a fiddly but functional trick for making Outlook prompt you when it tries to close. Create a message to yourself, hit the Options tab and click on the Delay Delivery button, then set a date long into the future. As long as that message remains in your Outbox, Outlook should prompt you whenever it closes that there are unsent messages in the Inbox, giving you an option to avoid closing. Hit the link for the full details.
Displaying A Prompt Before Outlook Closes [Windows IT Pro]