After realizing that it's only happening on forms where I'm editing text I remembered reading this blog post;

http://www.dotnetnuke.com/Community/Blogs/tabid/825/EntryID/235/Default.aspx

I gave it a shot and it seems to have help a bit.  I still get logged out the first time I've logged on but after that first time I'm able to stay logged on unless I start moving around the site alot.

It's probably not the fix but seems to have helped a bit.

I too am having this same issue.  I am running 4.0.2.  This is something that should be escallated as a serious bug.  If I would have known of this issue with IE, I would have used mambo or nuke PHP instead of DNN.  I thought since I am hosting on a Microsoft server and using the .NET environment and browsing and editing with IE, it would all work together.  I have noticed that if I log in as Host it doesn't log me out.  PLEASE HELP US DNN Project leaders, or at least acknowledge this MAJOR issue!!!

Found this:

This is a cookie related issue.  I recently had to troubleshoot something similar for a customer.  The min/max settings for a module get stored in a cookie.  If any other module is using a cookie to store information it will eventually reach the maximum cookie size.  When this happens the forms authentication cookie is deleted thus forcing the logout.  I have also seen this happen with a few other modules.  We have already taken steps to help eleviate this problem in the 3.6 release of ActiveForums. 

Aaron