What causes a cake to sink in the center?

I made the cake from the recipe, and had no problems with leavening. I first cooked a marmalade of the whole oranges (including the pith) and all the sugar and then followed the recipe as given.

But during the marmalade cooking step, the whole thing cooked down a lot. I started with 950 ml of water and 225 g of sugar, and cooked to 107 Celsius, which means that maybe close to 800 ml of the water evaporated. The rest was very saturated. I don't know how exactly you made your puree, but you mention draining it, so I can imagine it will have been quite dry.

Now, if you look at a classic pound cake, the ratio is 1:1:1:1 for flour, fat, eggs and sugar. We have 225 g of sugar here and a similar amount of eggs. But we are using much less fat. It is common to use a fruit puree to partly replace fat, but if we are staying with the original recipe, even after 30 min of cooking, we will have much more added water and fruit pulp than the missing 160 ml of fat. So the authors seemed to have adjusted the recipe for the additional moisture by increasing the flour to 325 g.

What I did was to add only half of the flour I had measured out, and then a bit more baking powder as I had already mixed the leavening agents under the flour. If you didn't adjust the flour but cooked down the puree a lot, you might have ended up with a very heavy, floury cake, which couldn't leaven and collapsed under its own weight. My advice would be to try reducing the flour next time and go by feel until you have reached a proper batter consistency.

A possibility would be that your cake ended up being too moist with liquid. Note that @rumtscho reduced most of the water out in her attempt.

If I recall correctly (it's been years) Bakery Master, Joanne Chang said something to the effect of:

It's not that cake collapses in the middle, it's that the cake holds on to the form better on the outside.

This the same reason that some cakes go the other way and dome up in the centre and why the bunt form has a hole in the centre.

What possibly happened to your cake was that the cake had a nice chance to 'cure' around the outside since heat was more accessible. In the centre, however, being the most buffered part, the cake remained mushy long enough to let gases escape before the protein structure formed strong enough to hold it up.

As others have said it can be because it is too liquid rich and therefore the liquid/flour ratio is not right. The other reason can be that the oven was opened too early. The rush of cold air can cause a good cake to collapse. Try leaving the cake for a bit longer before opening the oven and the structure should stay.