I was told by the craftsman to store it standing up but stuffed with either tissue paper or the bubble pillows it comes with. I will put a folded up (clean) towel in mine in a pinch if I am in a hurry when coming in and don't wish to dig out the tissue paper. I've had mine for 1.5 years and while the sides are "softer" it has not collapsed like Clemence would.
I let mine lie down in the box. All my bags get to rest in their own boxes