Zimbra seems to have fixed the problem in the latest release of the connector. I downloaded the latest version of Zimbra Connector for Outlook 5.0.9 GA Release from the Zimbra Downlods page. At least in my testing this morning on my computer, every time I exit Outlook 2007 the OUTLOOK.EXE process in Task Manager shut down like it should. I plan on running it on mylaptop for a few days before upgrading my other computers.
This looks very promising.