It sounds like a similar problem to the one I had, discussed here:
Never really got to the bottom of it, but it seems to be host related. On some sites I was finding the updates folder had failed upgrade files left in there, sometimes multiple folders of them. Sometimes it froze in maintenance mode, but it often never got that far.
I’d be interested to know if it will auto-update. With the last version release all my sites auto-updated perfectly (once I’d cleaned up the wp-config files).