Update.php still doesn't update my test site in beta 2 from 4.6.4.

Note that this is meant for 4.7-Beta2, but that is not available as a version yet.
This problem already existed in beta 1, but is still present in beta 2. My test site runs on Apache 2.0.55, MySQL 5.0.15, and PHP 4.6-PL1 (the current XAMPP distribution from www.apachefriends.org).
I had originally set up Drupal 4.6.4, but since I'm still in the testing phase, wanted to try 4.7 beta when it came out.
When I attempt to update, after backing up the database and replacing the old Drupal 4.6.4 files with the new ones, the following happens:

1. I open localhost/drupal/update.php, and am presented with the welcome screen of the update script.
2. I then click the "Run update" link.
3. On the next page, I am rpesented with the message that the version I am upgrading from has been automatically detected, and that I should not need to select a different version. To see which version the update script chose, I expand the "Select version" anyway, and can see that it shows me the number 129 in the dropdown list.
4. I then click "Update".
5. After a moment, I am returned to the welcome screen.

I can repeat these steps with both IE 6 and Firefox 1.5 over and over. It will always show me 129, the update button will return me to the welcome page, and no updates have taken place. If I put my Drupal 4.6.4 files back, the site still works as before, and when I try to launch the site with 4.7 beta 2, I get loads of error messages.