It stopped working for me and they were unwilling to continue to trouble shoot it and told me to use Galaxy.

That sucks! I know they stopped d updating GOG Downloader but it should still work. I find GOG Galaxy inferior when wanting to download games manually. It doesn't sort them as good as GOG Downloader.

Sorry, don't follow you. Logging in through the website is fine, so why can you not download once you have logged in to the website?

Logging in to the GOG Downloader is the problem but logging in to the site and Galaxy is working fine.

Browser download is not the same as Gog downloader. There are three options: Galaxy, Gog downloader, and going into you web account, and downloading the files directly from your account. Does not require any other software.

You forgot unofficial downloaders (at least 2 that I recall) and wget (or powershell equivalent). All of them should support resuming, with some requiring a bit more tinkering to do so.

Last time I tried restoring via a 3rd party download manager it wouldn't work. They change the URL for the download and if the download hasn't started by that point, it won't work.

That was a real problem during that period where there was no functioning download manager for any platform because they killed support for the previous one without making sure the new one worked.

Hopefully that's been changed to be a bit more lenient.

Now why won't it work for me using GOG Downloader when for other it's working fine?

Instead of passing the cdn url, pass it the game/en_installer one you get from the account page. Assuming the download manager can handle redirects correctly, it should be able to resume.
There was a thread detailing how to do that with getright, tell me if you want me to go digging.

What I found was that on larger downloads the download manager would take too long to start before the timeout on the URL expired.

It's not a particular problem now, because people can always use a Linux Mint live CD and install one of the Linux downloaders on that. I know that Lgogdownloader supports resuming.

I'd be curious as to why they change the URLs all the time and don't just create an individual URL for the person and require a login. Seems like that would keep the files secure while allowing people to use whatever download manager they like.

The URL is the same, the session id is different. Each session id is IP dependent, and valid for a few minutes. That means the CDN only has a session id to verify instead of username/password, and also that one can't give said URL to someone else to download.