BSinator: GOG exclusive, never happened to me on Steam or disk games or Desura before.
Fictionvision: My first thought is having Steam or Desura open in the background is causing network traffic and keeping your wireless adapter on where as a GOG wouldn't do so.
Do you have Steam and Desura closed when not playing games on them?
I think you missed the point with this post a while back (and a fewe others have said the same thing.
He was asking if you had Steam or Desura open whilst playing games from them but you answered
"No, I do not have either of those running at the same time as the game I'm playing from GOG." The point is that Steam and Desura will keep your internet connection open whilst you play if they are still running in the background when you play Steam or Desura games.
GOG does not do that so will not keep your internet connection open so it then times out, overheats, powers down of just plain gets bored and goes in a sulk.
So I think this is a non-problem. GOG is not disconnecting your internet - Steam and Desura are not allowing your internet to shut itself down like it wants to.
Go ask Steam and Desura why they are wasting your precious battery power by keeping your internet connection open when you are playing a game.