I just leave it running on my server
That might be the reason why it works. People who report that resuming doesn't work probably had to resume because they lost their Internet connection. The download tokens are probably bound to your IP, so if you have to reconnect and get a new dynamic IP, you have to request a new token. Maybe a download manager that allows you to resume even if the address of the file has changed would work?
When I say XGOG Downloader works fine, I mean I can unplug the ethernet connection in the middle of the download, plug in my mobile broadband and connect to that instead and the download resumes without a hitch. It has nothing to do with your IP, the XGOG Downloader just handles the resume properly for GOG's setup (and it doesn't require anything particularly special either, it does literally just request the original
download URL again, not the one you are redirected to, to get a new token/download url).
And by server, I mean a machine less than a foot away from my desktop machine. Not one in a data-center or anything like that.