Yes. We've confirmed the cookie is being set with the proper value. Now we just have to troubleshoot the issue where your session is not staying maintained before that timeout value.
For clarification, you're repeatedly saying that you've been "logged out", but that isn't the problem we're troubleshooting, right? We're looking as to why your session isn't being maintained. "Logging in" is the process of going through authentication where you verify who you are to the server, it authenticates those credentials, and then can "log you in", often storing your information into the session. The problem with the latter is that if you have code somewhere that is terminating the session or performing log out operation via improper misfire, this is different than a session that just seems to be lost at some point in requesting pages that are doing little more than presenting data.
Since you're not using subdomains, we don't have to worry about you navigating to other areas of the same domain. Let's try this:
Make a page that just outputs this:
<cfoutput>#session#</cfoutput>
If you keep reloading that page, do the CFID/CFTOKEN values change?
By the by, what browser/version are you using?