Themes disabled after a couple of clicks

The issue seems a duplicate of http://drupal.org/node/305653 but actually it is not.

[…]when viewing the themes selection page that all the themes are disabled even the default theme when several themes were in fact suppose to be enabled. We've had a site that has had it's theme switched back to the default when it wasn't suppose to be and we don't know why but believe it has something to do with this.[…]

This applies to my drupal, but in my case it has nothing to do with the update system.

I have now installed a new theme: Acquia Marina, but not enabled for everyone, just testing under user #1.
So two themes are enabled: the website default theme, and Acquia Marina.
As soon as I browse a couple of pages, Acquia Marina for user #1 reverts to the default theme.
The admin page at /admin/build/themes shows all "theme enabled" checkboxes unchecked, even the default one, see attached image.
So I have to re-enable the two themes, then go back to the site.
After a couple of clicks the themes get disabled again.

This is critical to me, hope you can help me… :-((

My website runs drupal since 2003, and today all modules and drupal core are updated to their latest version.

Drupal 6.15

Admin block 6.x-1.1
Auto Time Zone 6.x-1.x-dev (2009-Feb-21)
Backup and Migrate 6.x-2.2
Birthdays 6.x-1.0
CAPTCHA 6.x-2.1
Chaos tool suite 6.x-1.3
Counter 6.x-2.4
DB Maintenance 6.x-1.2
DHTML Menu 6.x-3.5
download_count 6.x-1.3
External Links 6.x-1.9
FCKeditor - WYSIWYG HTML editor 6.x-1.4
FeedBurner 6.x-1.0-beta4
Flag content 6.x-1.x-dev (2009-Mar-28)
Formfilter 6.x-1.0
Global Redirect 6.x-1.2
Google Analytics 6.x-2.2
IMCE 6.x-1.3
Javascript Tools 6.x-1.0
LoginToboggan 6.x-1.6
Mail Editor 6.x-1.x-dev (2010-Gen-28)
Nodewords 6.x-1.11
Page Title 6.x-2.3
Panels 6.x-3.3
Path redirect 6.x-1.0-beta6
Pathauto 6.x-1.2
Private Upload 6.x-1.0-rc2
Re: Comment subjects 6.x-1.5
Safari Search 6.x-1.0
Scheduler 6.x-1.6
Search 404 6.x-1.8
Service links 6.x-1.0
Similar Entries 6.x-1.1
Site map 6.x-1.2
Site verification 6.x-1.0-rc1
Skinr 6.x-1.4
Subscriptions 6.x-1.1
Taxonomy Access Control 6.x-1.0
Token 6.x-1.12
Username originality AJAX check 6.x-1.5
Views 6.x-2.8
Views Bonus Pack 6.x-1.0
XML sitemap 6.x-1.2