How to prevent Outlook 2010 home & business from closing

Let me explain my situation. I help set up computers in a small business office. They use Outlook 2010 Home & Business on their Windows 7 machines to do their emails. What happens is that for some reason ladies that work in that office have a tendency of closing the Outlook window, in which case it doesn't check for emails anymore and what I get is that they start complaining that they never receive emails :) I know, but it's not easy to explain the actual reason why they don't get emails... they continue closing it.

I tried this scenario myself and indeed if I click on the red X for the Outlook main window it closes without any warning or a prompt and the design of the Windows 7 taskbar makes it indeed hard to notice if it's running or not (the Outlook icon is pinned to the taskbar there.)

So I was thinking is there a setting in Outlook 2010 to show a warning before it closes? Or, can I somehow make it check for emails while it's main window is closed?

@Dsprague: Well, that is an interesting solution. Thanks.