App windows move spontaneously on display wake (2 monitors) - OS X 10.8.3
I'm guessing the 2nd display is not an Apple display.  

I believe what is happening is that the display is, in fact, going to sleep, but in such a way that the Mac thinks it has been powered off.  

Replacing the  HDMI --> DVI converter with an Apple Thunderbolt --> DVI converter is your best bet at fixing this.