If you’ve ever run more than one monitor, you know how messy things can get. Windows has come a long way with tools like Snap Assist and FancyZones, but it still struggles to make multi-monitor setups ...
Install ATI Tray Tools. Over or underclock your card with it by a few MHz. Set it to reset the clocks on resume from standby. That'll reset the video card and should resurrect your second display.