Thanks very much for this thread. My K7xxx 13" also was having a strange "go soft focus and then fade to black" issue. Opening the back of the cab, poking around, then turning back on caused it to work again... then randomly it would start going out of focus and slowly (10 seconds) get dim and turn off, yet there was still HV and I could hear the 15.75 KHz refresh.
I didn't see any bad joints, but did notice a few following back from pin 4 (of 8 pin) which is the heater that had been resoldered before in a couple spots along the way. I reflowed everything from Pin 4 (and pin 5 -- ground) all the way back to the flyback through the neckboard, the jumper wire, the 5 wire bundle down to the mainboard, etc...
Put back together and could not make it fail, even after pressing the neckboard, chassis or messing with the bundle of cords from the neckboard. Seems to be fixed now.