How to stop a sponge cake (chiffon cake) from deflating/sinking?
Many sponge cake forms are made with removable bottoms and tabs that stick up on the sides.

The purpose of the removable bottom is obvious, run a knife around the side and push the cake out. However, the tabs allow for a marvoulous technique when cooling your sponge cake.  

When your cake is done cooking and ready to let cool, you invert it without running your knife around the edge.  The tabs keep the pan above the table/rack and allow for the air to circulate.  Gravity helps to maintain the height of the cake because the cake is still stuck to the bottom and sides of the pan.  As it cools, the little stretching action from gravity gives you a higher/fluffier product.

It doesn't completely solve your shrinkage issue but it helps out allot.