OK, I think what you may have is your picture tube is right on the edge of working with the set's AKB, or auto cathode balance. All Sony tube TV's use AKB.
AKB is a circuit that attempts to compensate for aging of the picture tube (among other things), and if the tube isn't conducting enough (due to age), it will intermittently blank the screen or, in sever cases, not allow the picture to come on at all.
But if you are comfortable taking the back off of the set and making a minor adjustment, you can probably restore the picture for a while longer.
Take the back off, turn the set on to a blank channel (receiving snow). You will see a large gizmo with a thick red wire coming out of it going up to the glass on the picture tube. That's the high voltage (a.k.a. flyback) transformer.
On this transformer will be a small knob labeled "Screen." If I'm right, if you turn this control ever-so-slightly counterclockwise, the screen will blank off immediately. But if you turn it just a bit clockwise, it may fix your problem. Don't go too far with this control, just enough to make it work.
Try that, let me know if you have any other questions, and thanks for using JustAnswer!