There is no particular circuit block that delivers a flat line, the flat line is caused by the absence of vertical deflection, the horizontal deflection sweeps the beam across the screen, voltage at the probe causes the beam to move up for positive voltage and down for negative voltage, if the voltage is zero then the beam will sweep across the middle of the display.
Note that this describes how an analog scope works, if you have a digital scope then it will tend to approximate this behavior but they don't work quite the same way. Either way I'm not at all convinced that there is anything wrong with your scope, can you post a video of what it is doing?