Interesting. Can you add temporary FTP access? I can try debugging the process via editing the files, to see where it exactly fails. It is much more likely to be a firewall/blacklist or connection issue, but I think it is worth debugging nevertheless.
I found the issue, it was nothing major – the license key was activated for a different site (the dev domain of your site). Some development/test domains are recognized, but this was a completely different domain name so it passed by.
Somehow the license check failed, and did not deactivate automatically either.
I have corrected the issues and the update went through nicely.