Response from GOG...
Hello
Please use the GOG Downloader to download your games. This application uses different means of authentication than browser links, and using it is practically guaranteed to fix this issue.
Our browser download links are IP-based, to accommodate browser download resuming. This works under normal circumstances, but, unfortunately, we have learned that if a user's connection assigns a different IP when connecting to our site, and then a different IP when the actual download is initiated with our file hosting provider, an IP mismatch occurs, resulting in the 403 error. We are currently unable to resolve this issue, whilst preserving our users' ability to resume browser downloads.
It may be possible for your network administrator to modify your network setup so that you are issued the same IPs for both GOG.com, and our file hosting provider's servers, which you eventually get redirected to. Unfortunately I cannot guarantee if this will work, nor if the network administrator would agree to making such a change.
We apologize for any inconvenience this may cause.
Regards,
JuriJ
GOG.com Support