I think the login is held as a cookie. I believe that's how Windchill knows when you've logged in or not. I have seen other places that to switch users in the browser can be done by deleting said cookie(s).
With no access to the PTC code, it's only a guess that something is wiping the out the cookie, forcing the need to log in again.
You don't mention what browser is being used. I haven't anything specific in mind, but that's where the cookies are stored and maybe others will notice something about the particular browser. Also, Windows version would be a clue as well.
What happens to the user if he changes to 'offline' except for specifically using the connection to Commonspace?