Seki in superko
In the 4-move (3-move?) cycle sending two returning one, Black plays two stones, White only one. With territory rules, this costs Black one point. After some (finite) number of cycles have been played, White could simply admit Black's claim that the white group is dead, and still have enough points to win. So Black does not start the cycle.
(Why would Black initiate at all if costs one pt per cycle?)
Chris L After one cycle the board position will have been recreated. Is this not prohibited by some form of ko rule?
chrisg I'd be interested if someone could add a reference to a page explaining if this isn't a seki, and under what rules.
El Draco With the positional superko rule, it would be prohibited to complete a cycle [as Black's recapture would do], but with situational superko, after one [such "]cycle["] it's White's move instead of Black's [and therefore not yet a cycle under those rules]. If [s]he plays somewhere else, Black can try playing there again, with the same result.
There is one devious way Black could play however, which is playing a ko threat right after White captures the two stones. After this [and his answer and his recapture)], White can't pass, lest Black plays a1 again and White may not capture the two stones without repeating a previous position with same player to move.
This way, Black could win if he has more ko threats than White has moves to play. If White plays [in his or] in Black's territory just to not-pass, Black must pass [if he ran out of ko threats] and it wouldn't have cost either player a point. If White has no legal (or plain dumb) moves left however at some point, and Black has at least one ko threat, Black can win.
Correct me if I'm wrong, since I just thought this up. ;)
But you are not alone. I think Frank Janssen was the first to have that idea in the '90s. See Rules Beast 1.
Robert Pauli: Added the bracket parts for clarification. Not to disturb the flow, my comments follow here:
 Correct, but nevertheless positional superko can be exploited with the same trick.
 Shouldn't he prepare for the ko fight instead of repeatedly sending two? Black could drop stones into white's territory (of no expense as we're assuming area rules). Since white can't expect him to agree on them being dead, he has to capture those he can't afford to stay, wasting precious plays for the ko fight to come. Similar to no-pass Go, his drops also should destroy his eye shape to bring down the number of eyes white can form. Black should also divide his territories to prevent his to drop in later. On his part, white should remove as much of his ko threats as possible.
 Well, assuming Black didn't start the cycle before his first pass (otherwise considering the second pass makes no sense), already his recapture at a2 (right before his second pass) returns before his first pass and therefore is forbidden. So Black plays the ko threat instead, as correctly follows.
Seems to be true if his ko threats are unremovable. After each of his plays white again is able to complete the cycle with a pass (he won't waste another play). Then Black has to spent another ko threat (after his atari and his capture) to spoil that ability again, just as he did after his first pass.
But now imagine white's two-point vital eye he could drop a stone into, threatening it. Since white could prevent that by a drop of himself, that's one move versus one threat. Nevertheless he will win if he starts.