Found this from another sys80 casualty....Sounds exactly like what you're experiencing:
I am currently working on a very similar problem with my Gottlieb system 80B
game, Big House. I have determined there are specific switches on the
playfield that cause the speech and some sounds to quit. You should see if
the same happens with yours. The list of things that are NOT causing the
problem include: switch isolation diodes, poor ground connections (although
I would do John Robertson's suggestions, www.flippers.com ), game roms,
sound board 6502 chip, and the power supply for the sound board. I am going
to start looking at the op-amp chips on the sound board. I will let you
know what I find.
By turning your game off, and then back on, you are rebooting your sound
board as well. I would imagine you are crashing one of the 6502 sound
circuits during gameplay (I know that I am, using the oscilloscope), and
then by turning off/on you restore the crashed circuit.
Take off the translite, and turn your game on. Is the LED flashing on the
sound board? (probably yes). Play the game enough to lose the sound, or
take off the playfield glass while a game is playing, and try closing
switches, to see if you can find cause and effect. Is the LED still on?
From the above, a good test would be to see if you can replicate loosing the sound by hitting a certain switch. Play a game and make note of when the sound goes out and what the ball is doing. See if it is common to a switch or a particular sound being played.
Another good idea from Cliffy (I read on RGP) is when this happens spot spray some freeze spray onto each IC to see if the sound comes back. That would isolate an IC heating up.