Asymetric Kite.

sailor girl !   the closest i can think of is that is another sail that the crew trim

I'll have to disagree with you on that ... asymmetric spinnakers are nothing like jibs. Hope I'm not the only one who thinks that !

A diagram I used to use when I was teaching .... might come in handy ....?

I just thought of another way the kite can collapse - its probaly more relevant to the 4000 than any other class due to the length of the pole.  In lightish winds if you bear away too quickly the sweep of the pole is to leeward and the kite is backwinded.  Naturally this doesn't happen in a decent breeze and it doesn't happen anymore to me since I've learnt that such a big heavy boat is best handled smoothly.  But I do use this effect to advantage when I gybe, I always wing wang the pole up to windward after the gybe since this scoops up a spinnaker full of air which gets the kite flying nicely out of the gybe.

One other thing is that you should look at where the kite collapses first, it is curls at the front then either you let it out too far or the helm is sailing too high. If it collapses first at the back or curls at the back and gets horribly twitchy, swinging round to windward and things then you helm is sailing too low. you should both talk about it when that happens.