Mentioning mental health in a supplementary application essay
I'm pretty sure you misinterpreted the question. I would think that they wouldn't (dare) ask about your personal failings or mental state. The question as I interpret it is about a setback in the research itself. Suppose you don't get enough subjects to properly carry out your experiment as proposed. What do you do. Or you learn something part way through an experiment that invalidates it and you have to go back and revise. 

If you never have setbacks then I'll guess that you aren't trying hard enough to get to the important questions. For a mathematician to be able to prove every proposed theorem says those theorems aren't very consequential. (I've been in that place, actually). 

Focus on the research, not your own psychology. Your application should clearly indicate that you are absolutely the best person for this position and will obviously be a success. Moreover you are flexible in overcoming the unknowns that pop up during the execution of it.