Looking into it, seems like a few Allied leaders were being treated for mental health, Churchill being the most famous. But I never hear about that on the Axis side. Did any German/Japanese/Italian politicians or generals suffer from mental illness?
Suicidal tendencies were a sufficient problem in the SS that Himmler made a point of saying that funerals shouldn't be given for officers who committed it for "trivial" reasons. Between July and September of 1942, 30 members of the SS committed it. One particular case was a SS Brigadier named Fritsch who killed himself in 1944 because he cheated on his wife and felt guilty. Himmler ordered the SS insignia removed from his headstone.
Source: Suicide in Nazi Germany By Christian Goeschel https://books.google.com/books?id=oysUDAAAQBAJ&pg=PA61&dq=SS+Officers+depression+suicide&hl=en&sa=X&ved=0ahUKEwiNkPTNppzRAhUH3IMKHdrjAR0Q6AEIGzAA#v=onepage&q=SS%20Officers%20depression%20suicide&f=false