So I have been using Gameboost with Oblivion and figured that I would use it with Skyrim, but - a strange thing...

When I have Gameboost in the system tray, I fire up the Steam client and click on Skyrim to play it - cool, Gameboost fires up and does its thing.
BUT: when I then get the Skyrim game menu up and click to play, Game boost turns off.

There doesn't seem to be anything I can do to stop this from happening either, does anyone know...?

Cheers!

Are you talking about Gamebooster 3? I'm using that and I set it to game mode manually, then manually launch Skyrim from the Steam.

I think what's happening is that GB thinks that the game ended when the launcher exited. Try the manual method.