Monitor flickering / flashing to black

One of our Mac Pros has developed this random flicker, where a horizontal part of the screen will go black for a tenth of second.

It's a Mid 2010 Mac Pro with a Radeon 5770 1024MB video card. The monitor is a Viewsonic VG2228 connected via DVI cable.

Video here: http://youtu.be/I1gM8c73HjM

I've swapped the cable and made sure the connections where solid, but I don't have any spares to swap monitors or video cards. I'm not sure what else to try. Any ideas?