No, DVIRecover will not help, but you could try the power cycling trick:
1. Turn off the computer and monitors.
2. Disconnect everything (including power cable) from the blinking monitor.
3. Wait ten minutes.
4. Reconnect everything and see if the problem remains.
Another thing to try is posting in xtknight's LCD sticky thread or amending your thread title asking for help trying out custom timings with PowerStrip (shareware?). IIRC, sometimes adjusting the "porch" values has stabilized monitors. IOW, I have seen such threads but have no personal experience with the problem.
You could also try disconnecting both monitors and using the blinking monitor as your primary (and only) display for a few days. If the problem exists, then at least you have eliminated multi-view as the source of your problems...
Otherwise, your problem is probably a failing monitor, cable, or video card.
The power cable might even be at fault. I once had a satellite modem with a faulty power cable (of all things!).