It's a workaround, but you could enable a virtual desktop in winecfg. The game won't be completely fullscreen, but it won't mess with your screen settings either. Turning the second screen back on through a tool like lrandr after having started the game works too. This is more of a video driver related problem than a Wine one, though. If your driver comes with a settings tool (think the ATI Catalyst Control Center for example), open it and see if you can find a way to always keep the second screen enabled.
