While upgrading a couple of different Drupal (5.x) sites, I ran into an annoying issue where the update.php script just redirected to the sites homepage after the "Select Version" page. The server in question has PHP's mod_security enabled which has caused some problems with other sites in the past, so I think it's related to that, but I'm not totally sure.

Any way, the fix is to add the following line of code to your update.php script before line 794