We have had an arc furnace in service for about two years and haven't had any problems yet with the cables.
We perform periodic IR inspections to ensure we have good connections at both ends of the cable. (as well as the rest of the high current system) We also retourqued connections a while after installation but found few problems. I would say the thing to watch out for is mechanical wear of the cables due to flexing with furnace movement, as well as wear from bouncing around during unstable arc operation at the beginning of heats. (Evidenced as previously stated by outer damage and leaking)
I'm curious to hear why conductivity of the water is so important. I've had little concern for the conductivity of the water, other than to ensure each phase is balanced to ground.