As a rather touchy subject, and the Navy being, especially among the Wardroom and Captain ranks being sometimes a rather closed fraternity, this isn't something that really has much scholarship on it. Many officers who wrote memoirs tended to gloss over some of the more morbid topics, and nobody was really going around studying how survivors acted their grief out post war.

That being said we do have a few high profile Captains here and there where it comes up. Most notably Captain Charles McVay III, who as skipper fo the Indianapolis was the only CO of a Navy ship court martialed for its loss in WW2. For the rest of his life he was reportedly deeply impacted by the vicious and terrible letters and calls he got from relatives of the dead. To the point where it very much is believed to have contributed to his suicide. That is not to say he was blamed universally by the survivors, many contributed greatly to his later exoneration and clearing of his name by act of Congress in the 90's.