Even with an analog scope, when probing address lines you should see them toggle, at least a short blip. Go into slow time sweep mode (1s/div or so) , turn the display bright and when you press store you should see the related line toggle (does not necessarily have to be A0, even though that would be logic). I am afraid, since the schematic is so simple, that if its not the trace (sometimes on these KORG synths given the PCB is of cheap quality, they have cracks, have even seen it on ground reference planes) its either the CPU or the SRAM that needs replacement.
I dont understand though, why at this stage you have not yet ruled out the traces. Thats just ohms measurements, and since your problem is stable, any interruption would be stable too.