Usually it's the lower hose that will do that if the reinforcing spring is missing. Normally the upper hose doesn't come with a spring. Get a replacement hose...that one is defective.  

 Sounds to me that the System is going into a Vacume. Everything was fine when You ran it and then when it cooled off the Hose colasped cause its under a Vacume. I'd look at the Radiator Cap. Hey, at Least You know You don't have any Leaks!

As your coolant is heating up, it blows the extra into the overflow tank.  As it cools down, it sucks that extra back into the engine.  That is controlled by the radiator cap.  If the hose is original quality, maybe the radiator cap is sticking, or the return line is plugged.  But most likely the two opinions above are correct.  It is just a cheap hose.

Larry

it most likely is the hose going from the radiator to to overflow is bad. had this problem withna car i had and as soon as i replaced the hose it was fine. hope this helps.

I would have to agree with the rest, Cheap hose. I just replaced my water pump 2 weeks ago and replaced the top hose, themostat and radiator cap, But my hose when running stays inflated and even after cut off stays with pressure till it cools down but does not go flat. The cheapest fix is bad new hose if that dont work I would go to the overflow hose, and make sure your lower hose does in fact have a sping. the stuff they are selling at the auto parts round me were totally incorrect So you have to be prudent and ensure you are getting the right part! williammoore22008-10-05 06:45:06

Thanks for the info. It was the rad cap. Sometimes is easy to forget to check the simple things and assume its something major.