Why does Internet Explorer not call DLL_PROCESS_DETACH on my DLL when I call ExitProcess?

A customer asked a question, but as is often the case, the question was much more telling than the answer. We have an Internet Explorer plug-in which calls to force Internet Explorer to exit. We found that when we do this, our plug-in does not receive a notification. What could be preventing our plug-in from receiving the notification? As w...