If you specifically mention that you need to pause your downloads, and the existing system doesn't support it, then at least you'll get a solid response one way or the other.
If the GOG Downloader is not working, it may not just be the GOG system - it could be possible that your ISP is still using some sort of proxy service, which can interfere with resumable downloads. Very few ISPs do things like this these days, but it might not hurt to check with your ISP if a "transparent proxy" could be a problem.
Sorry to see you're having problems with our downloader.
We're working on updating the downloader sometime in the near future.
For now you could try following the steps in this forum post in the gog com downloader sneak peak topic. You could that way at least backup what the downloader has already downloaded.