OK, I looked around for a short while like I promised......
I compared the files and I am wondering where you got PivotX version from? It is a 2.3.11 version but several files on your site are different from the original files.
In the templates_internal folder and editor_wysi there are differences. How come?
I reinstated the ajaxhelper.php (with the same change you made for the 42things bit) because the version that was there now was rather old and very incomplete.
Alas it did not help.
Then I checked your folder rights. Did you set them according to the installation instructions? Apparently not because a lot of files in those folders were not 777.
It is described on http://book.pivotx.net/page/1-2
So I changed that too but also to no avail. Every change you make to the config seems to be OK but when you change to another section of the dashboard you get logged out.
I managed to switch debug on by editing the config file and upload that.
Most of the times when I even want to look into the debug log I get logged out there too.
I once saw a CSRF error and an error that user should be logged out because no one was logged in.
So I advice you to resolve all other differences that are non-intentional. This will probably not help but you'll never know.
Be sure to clear cache and the likings.
If problems persist try to PM hansfn and see whether he is willing to debug your problem.
Please remember that development and functional support of PivotX has long been stopped and really only the bare necessities are still debugged.
Sorry I couldn't be of more help............
Quality is in the detail of things............
Want to change or update your PivotX site? Mail or PM me!
I can also convert your site to a Wordpress site!