I am running Mac OS El Capitan on my rMBP. As it stands, Jan 26 2016, my creative cloud app version is 220.127.116.11 which according to these release notes came out on 11/26/2015. Release notes for the Adobe Creative Cloud desktop app
Are there some updates that it won't download, or if I have a problem how can I fix this?
Ideally Creative cloud update should be installed itself. But for some reason if it does not update itself you can uninstall creative cloud desktop app and install it again.
Install it using Download Adobe Creative Cloud apps | Free Adobe Creative Cloud trial