Since it’s not an option for me to disable the firewall, I manually updated gp premium by replacing the files in “\wp-content\plugins\gp-premium” with the new content in the gp-premium zip-archive.
Problem is solved for now (even though I would prefer to update the normal way).
The error saying “could not copy” generally means there’s a permission issue, or maybe a disk space issue – your hosting should be able to find and fix it for you 🙂