30" Cinema Display flickers after extended sleep.

I have a 2008 Mac Pro hooked up to a 30" DVI Apple Cinema Display (I guess that's what it was called back then), and if I let it sleep overnight, when I come in to turn it on the next morning, the screen just flickers intermittently. Once I unplug the monitor from the power supply and plug it back in, it works fine. I've tried swapping the power supplies with one out of the office next to mine to no avail. Any fix to the problem?