The repetition is getting to me too. And at first I tried to focus on the variations between the cycles... but that didn't seem to lead anywhere. So now I'm wondering if there might be clues of things to come in some of the things that happen exactly the same way every time. For example, she always introduces the 2 guys as her subordinates at the pool (maybe she wants that to change?), she randomly offers Kyon and only Kyon a meatball thing (I don't know what its called) at the festival (special treatment?). And he always wastes the last day of summer (seems like a good time to ask her for help with his homework, or do something else with just the 2 of them... anyway, that last day seems very significant).
I don't know... just trying to entertain myself while waiting for this infinite loop to end >.< I hope Nagato stops just observing and helps Kyon at the start of a cycle; it seems like their only chance.