This is an old dilemma that was also discussed on L19 (here for example), and may be a simple misunderstanding of the pass for ko rule. The rule forbids recapturing in a ko that the player have not passed for, but it doesn’t clearly require a new pass for each later recapture in the same ko.
This is definitely an unclear point in the rules that need official clarification, without which we can only speculate. But the commentary on 7.2 gives some hints:
When the game stops, ko recapturing also stops
If a player whose stone has been captured in a ko has passed for that particular ko, the situation for that ko is the same as if the game had been resumed: the player may now capture in that ko again
Which seem to suggest that ko recapturing “stops” once, at the normal game stop (and not at each ko capture by the opponent), and passing for a ko “resumes” the game wrt that particular ko.
And OC, if passing for a ko is only needed once, there is no endless cycle in a double ko seki (as it will revert to a normal double ko seki after one cycle).