I've had issues with this as well, where the auto-update no longer works after a manual update has been done. I took a look at another OSClass installation which I did auto-upgrade. I checked the file permissions for those.... all folders were 775 and files were 644.
So, I figured if I applied to same CHMOD changes to my "manual" installation of 2.3.1, the auto-upgrade would once again work. Nope. Then I took your advice Juan and changed every single file and folder to 0777. Still does not work, and that does not make any sense to me.
It is worth noting that I'm using both a Windows 7 and Windows XP computer, neither of which preserve file permission settings during manual site updates, hence why I believe this problem occurs in the first place.