I think dsugarman meant "at least once over any FINITE amount of time", in which case each prisoner might visit again an infinite number of times, but it can be arbitrarily many turns in the future.
So, if you wait a finite amount of time (in this case a "few" billion years") it's possible that the visiting condition might not yet be satisfied.
So, if you wait a finite amount of time (in this case a "few" billion years") it's possible that the visiting condition might not yet be satisfied.