Do not assume that anything discussed in this document applies to these monitors since much of it does not. What I have described so far applies to all vector monitors. Knowing how these things work helps greatly in trouble-shooting. The monitors make their own positive and negative DC from AC inputs so a reasonable thing to check would be the power supplies. One of the main root causes of color vector monitor problems is game lockups causing the monitor to go extended periods with no input signal which fries it in short order.
Vector monitors are also fussy about the quality of certain transistors.
The X and Y deflection circuits are very much like audio amplifiers and tend to be hard on the big transistors used in the final stages of amplification. If you lose one of these transistors, you lose deflection in 1 of 4 directions depending on which transistor goes out. There is another circuit in the Atari stuff that is very important called the spot killer. The phosphors will become permanently damaged if the beam stays in one place for too long. When the spot killer is active a red LED on the deflection board lights.