Title.

What game?

Are you using the galaxy client, or normal offline installers?
I always recommend you download offline installers from your account here.
https://www.gog.com/account

I'm assuming Galaxy lists the error: "Save sync failed" when you exit a game and the client tries to upload your new saves. At least that's what has had happen to me in the past. That's a server side issue, and the only "fix" is to wait for somebody at GOG to restart the server, or solve the issue if it's something else more serious than that.

Again. Make sure to download your saves as extras after you have played. It happens, and it goes back to normal by itself at some point. I had lost my progress for a while but then everything was restored.

GOG goes out of their way to make sure that Linux users do not experience these issues.

By not making a Galaxy launcher for Linux.