Display flickers (goes black briefly) -- not Thunderbolt issue

I have an Apple cinema display circa 2009 that I am using with a 2009 MacBook Pro. The display flickers briefly (goes black for a second or two). This has always been an issue, but has gotten worse since adding a Kanex display switcher. I've tried switching the energy saver graphics preference, which didn't seem to make a difference. I have hooked up my laptop to another 2009 cinema display and don't seem to have the flickering issue, which made me suspect a hardware issue with the display. However, when I hook up another 2009 MacBook Pro or PC laptop to the display (using the Kanex display switcher), it doesn't seem to have the issue, so maybe it is an issue with my laptop and not the display. I have access to another cinema display, so I could just swap out the display, but if it is an issue with my laptop and not the display, perhaps it is only a matter of time before I see flicker with a new display? Or maybe it is somehow the particular combination of laptop and dispkay that causes the issue?