Most likely the CRT is getting a bit weak. these units shut down when AKB (auto kinescope bias) is not satisfied. Generally you can get more life out of it by increasing the G2 voltage, which is controlled by a pot on the flyback. The bottom one, the top one is focus.

Turn it up to where it will stay on, but not too much. Darken the room and set it so there is no "slick screen" under the video, lower the brightness and contrast (or "picture). set it right to the edge, and then lower it just a hair.

Something is in error here. When there is a fault in the horizontal drive, usually the horizontal output will fail, being shorted. This will sometimes cause a power supply failure that makes the set too expensive to repair. this is what the engineers were after of course, keeps them in a job. That's why they won't even let the set run if the CRT gets a little weak. Sony did the same ****, but they didn't all shut down, they just never produced a picture. Later models did shut down if any of the guns in the CRT got weak. This was how they sold TVs.

So, something was amiss. you did not check the transistors with a meter ? Waht kind of transistor checker is it ?