Several years ago we purchased two identical systems, and when the first one was set up the monitor displayed severely "off" color possibly like what's described - except it was permanent. A call to the builder suggested checking for bent pins in the connector - which proved to be the problem. On checking the other system, which was still in the box and still had the shipping protectors on the cables and connectors, we found the same pin bent on the other system, apparently by whoever put the little shipping caps on. The "pins" in this case were little more than a stripped end on the cable wires, extended through a "terminal block."
Since a "no-connect" like we had would produce a constant problem, rather than an intermittent one as described, it's more likely an intermittent loss of signal on one or more of the signal lines. As suggested before, cold solder joints are famous for such intermittent interruptions. The suggestion of swapping monitors or computers to isolate whether it's the monitor or the computer, if possible, would be good.
Another remote possibility - probably very remote - is that external magnetic disturbance can cause color distortion, although more usually there's quite a lot of "bending" in the image as well. When we hooked up a jury rig next to the stereo rack to archive some old vinyl records, one of the stereo speakers "blew away" the colors on the PC monitor until we relocated things. It would be difficult to imagine a sufficiently powerful "magnetic field device" that wouldn't be immediately identifiable, and pretty much constant unless you move hardware around; but it's hard for me to imagine the conditions some people describe for their systems, so I suppose nothing's impossible.
Our current monitors seem much less susceptible to external EM, but there's still some variation from one monitor to the next. On one older one, I found it almost impossible to "measure" images on the screen with my trusty 6" metal scale, since putting the (slightly magnetised) scale close to the screen would make the image move and distort. Our current monitors seem immune to this effect. (I change monitors much more often that I change my obsolete drafting tools.)