Why do my dual monitors stop responding?

Dell Optiplex 980 with ATI Radeon HD 3450 and two monitors. Overnight, the monitors stop displaying, even the screen saver, and won't redisplay when I move my mouse. If I log in blind (i.e., press Ctrl+Alt+Delete and enter my password while the screens aren't displaying), my Windows desktops appear as expected--except there is no mouse cursor. If I lock the computer again, then once again the screens go blank, rather than displaying the prompt to unlock the computer. For some of my coworkers, this happens even during the day, though for me, when I step away for a couple of hours, the screen comes right back when I move my mouse.