The correct answer to this open question is the following.
Although there are no options attached or further references, we can comment on the following.
I think some of the challenges facing those restoring the Hagia Sophia church in Turkey are the following.
First, the budget needed to continually restorative the impressive building. Next, the qualified persons to do it. They need specialists in engineering and art to do the kind of conservation needed.
For a monumental structure like Haga Sophia, it is required to have a high budget to do permanent maintenance works as a preventive measure, as well as to correct the problems caused by the pass of time such as erosion, cracks in the walls, humidity.