Have you checked it with an external trigger signal as well? Although I doubt that it makes a difference, but might worth asking.
Check the capacitance of the electrolytic caps. I doubt they cause the whole circuit to fail, but still a good idea to check them.
According to what you said, I'm thinking that the differential amp block in the middle might have some fault to it. There's a lot of components that can cause such a voltage drop, most probably a semiconductor's junctions are shorted. You should check the input FET (TR401) for good measure, and the differential pair transistors (TR404 and TR405) by desoldering and diode-checking their Base-Emitter and Base-Collector pins (Gate-Source for the FET respectively. If it's a JFET, don't be suprised if Drain-Source is shorted, that's how it should be).
If all transistors turn out to be good (i.e: have an actual diffusion voltage that you can measure, ~0.5-0.7 volts for silicon transistors), your next bet could be the logic circuits. Take one chip out, turn the scope on (high voltage, be careful! Don't even try to fiddle around the CRT while it's live), measure the voltage again. If it's still bad, solder in a socket, put the chip back, and try another one (it's good practice to socket your ICs, but not necessary).
Best advice I can give. Maybe some CRO gurus can give you better tips on this. Gotta tell, you're a lucky bastard to have such a simple schematic design in your scope there, I rather like it in fact.