thats why you dont let your kite hang around 12 oclock. any advise you might have gotten about above your head (12 oclock) being a good, or safe or "neutral" place to put your kite, for any reason, is bad, and extremely outdated advise. (wasnt actually good advise back in the day, either)
if you cant save it, let go of bar and let it fall depowered. if you are on the beach or near downwind obstacles, definitely dont try to save it (unless you know you can, based on experience, which you dont have enough of yet). in that case, disable the kite onto the leash (aka, quick release) it will fall lightly with no power, you can easily reset and keep going after..
dont hesitate to disable the kite when that happens and you are around the beach, shallow water, or dw obstacles. that should have been thoroughly covered and practiced in you kiteboarding lessons.
as for techniques to stop the fall and try to save it: what others said. it is different every time, line tension is the key, sometimes you can, sometimes you can't, you will know from experience.
this is also an easy time to snag a line around your neck, harness, bar end, or other things, or develop a line tangle on the kite, so be aware.
[[ edit: wow, i need to start reading other peoples posts more often and not assuming they are full of sketchy advise, there are a ton of good responses in this thread, sorry for the repeat info]]