I can't help with the OS logging you out, but I found a secret in SAP.
It also automatically logs you out after 10 or 15 minute of inactivity, unless ..... you have a long text screen open like the one pictured below.
Doesn't matter which one, as long as it's long text, white, and opens from an operations screen.
As long as that long text screen is open, SAP won't log you out.
i usually run two sessions all the time, the one with the long text screen in the background.