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.