I couldn't find a solution so here goes...
In reference to this bug... http://www.phpbb.com/bugs/phpbb3/54075
Using the Auto Upgrade to upgrade 3.0.5 to 3.0.6, it was stuck in a loop trying to merge (in my case) files /includes/session.php and /includes/ucp/ucp_register.php. No matter what I selected (merge, keep new, or keep old), those two files kept on appearing. I had a few mods and I didn't feel like doing a new install and reinstalling each mod.
Download (save) the merged files. I saved the above two newly merged files into a zip file. I also verified that the two files in the working directories did merge. You don't really need to save the files as the files are already merged in their directories, but it's good to have a backup.
The workaround is to Edit the /install/update/index.php file. Remove the filenames from the array that is causing the looping. In my case it was session.php and ucp_register.php.
Select Check Files again. It should be successful.
Note: I had to use Easyphp
for an offline update as I was getting 500 internal server errors. I used Easyphp 5.2.10 as 5.3.1 brought me to a blank screen