I just wanted to come back in on this topic, even though it is an old post.
Through researching another instance of this issue on a site using both the Url Master module and the Markit Slideshow on a child portal, I worked out some more relevant information.
In the case of the Markit slideshow, the symptom will show up as an immediate logout once logged into the child portal. This will occur on any page that has the slideshow implemented as a module. It may be incorrectly diagnosed as a logout on some other action (ie, click on another page, try and edit content, etc). The problem is that the user is logged out immediately after viewing the page. The cause is that the .ashx requests made by the Markit module cause the logout when the Url Master module is installed.
These .ashx requests are for resources like cssHandler.ashx, ImageHandler.ashx and perhaps others. Each of these calls passes a long querystring to the handler. It's not clear ot me what these calls do, and it's not really important anyway. What happens is that these calls get processed by the Url Master module, and that causes the user to be logged out. I don't know the exact cause, but my guess is that because they are made to the 'root' of the site (ie example.com) then the incorrect portal is loaded for the authentication (ie example.com/child should be used) and the authentication code in DNN logs out the user for requesting the wrong portal.
The solution is to stop these calls from being processed through the Url Rewriting code. Stoppign them being processed prevents the portal settings code from being run, which prevents the authentication code from being run. Thus the calls are made anonymously, and don't interfere with the authentication.
So, for the Markit module, you need to add on a regex pattern to the 'ignoreRegex' field. I've detailed this in a KnoweldgeBase page for the module here:
Url Master / Markit Slideshow Settings - I haven't put the settings into this forum post as I try and keep a canonical resource for this type of thing should future releases change this.
For other modules behaving in a similar way, the solution is likely to be similar. First, try and identify which requests might be doing the logoff action. If you trace with Microsoft Fiddler, you'll often see a 302 instead of a 200 for some requests in the page. This is a marker of something to look at - the 302 is caused by the logoff code redirecting back to a different page. ALternatively, try removing/disabling modules on a module-by-module basis until it stops logging off. If you find which it is, then look at the requests for that module more closely.
Putting a matching expression into the 'ignoreRegex' pattern means that, for the purposes of Url Rewriting (and by extension, portal identification and portal settings loading), the request will be totally ignored. This is often the way to solve an issue like this.