The degaussing circuit has a bad solder connection, most likely. There are devices (known as thermistors) in the degauss circuit that work thermally--when the monitor is cold, just turned on, part of the inrush current (the power-on surge) is shunted through a coil around the outside edge of the picture tube (CRT). This provides a magnetic field that demagnetizes (degausses) the steel-alloy shadow mask that non-Trinitron CRTs use to keep the electron beam from landing where it shouldn't--if it's magnetized, the colors are distorted. As the devices warm up, one lowers its resistance (negative temperature coefficient--NTC), so less current goes to the coil. Another device, in series with the coil, increases its resistance (positive temperature coefficient--PTC). The net effect is that the magnetic field (flux) fades away with time and the shadow mask is left demagnetized. The NTC thermistor dissipates a fair amount of heat in some cases, so its solder connections can crystallize, especially if they are a bit "dry" (not enough solder) in the first place--or the part itself can fail. This sort of thing can happen with any brand or model of monitor, so I'm not blaming Korea Data Systems particularly...

You have two options. One is to have the device resoldered or replaced. A TV repair shop or any competent electronic technician can do this. The easier "fix"--one you can do yourself--is to open the monitor and simply unplug the degaussing coil. As described earlier, the coil surronds the outer edge of the CRT, just behind the bezel. It's wrapped with black tape and has a pair of wires coming out of it. These wires plug into the main monitor printed-circuit board with a connector that may have a simple latch on it. The thermistor, by the way, is usually right next to that plug. It usually looks like a small, black cube.

Hope that helps! At least you know what the "deal" is.