The ones I've worked on usually have dry/cracked solder joints on the 9 way D-range connector at the rear of the monitor.
Movement of the monitor cable creates stress fractures on the solder joints.
As mentioned above, dry joints on the line output transformer are also very common, and possibly the same for the chopper transistor and other power devices.
One of my 1084S dropped the red colour as Cybereye said. That resulted in a yellow coloured display. Been too slack to look at this one yet :-)
Does anyone know a quick fix to this common problem??