In my case it was permission issues on some of the files and folders on the site. Hosting had to correct that for me. Still unsure of what caused the permission problem though because all previous automatic upgrades worked perfectly fine. When this happened, even manual uploading wasn't working.
Since your error says permission denied in it, it might be worth putting in a ticket to your hosting and see if that could possibly be your problem too.
My hosting support initially told me that the upgrade was timing out and wordpress was at fault. But they eventually dealt with taking care of the permission problems on all the files and folders and the upgrade worked correctly. Even plugins were failing to complete upgrade and a single plugin timing out just didn't seem logical.