More info may help...
Are these machines that you just got and have always done it, or have they just started doing it?
What changed immediately before they started doing it?
Power out due to a lightning strike or surge? Move machines? Add a power bar or extension cord? Similar enhancements or bullet proofing to the same circuit board in each machine?
What do multimeter voltages look in the circuit? Do you have schematics to know what the voltage levels should be around that circuitry to investigate more?
I don't know much about Flash Gordon... is it Bally as well and using some of the same circuit boards.
Essentially my question is if they are really acting the same way, and started doing it at the same time, what's common to both machines?