Second display on 2012 Mac Mini flickering constantly!

I have two displays going into the Mac Mini, one is going into the HDMI port which is working fine. The second display is going from a DVI to Mini DisplayPort adapter into the Thunderbolt input on the Mac Mini. It gets recognized but is unusable because it just keeps flashing on and off every few seconds! Please help! Brand new Mac Mini 2012 2.6 i7 16 GB ram

Thanks!