We just recently put a new website together using our host’s one-click install method. Instantly, the site needed something like 30 updates, most of which were to theme files.
So, I just clicked “update all”. Then, all of a sudden, my whole site was in maintenance mode and I couldn’t do anything. I did a little research and found this article about taking wordpress out of maintenance mode, this helped quite a bit as the site instantly came back to life.
I realized that something had gone wrong during the updates of the themes, so I went to my FTP program and made sure that the wp-content/themes/ directory had 755 permissions for the directory and all of its contents. Once this was completed, I told WordPress to attempt to update all the themes again, and it worked great!
I hope this helps you as well.