A legal action against the U.S. military probably doesn't stand much of a chance of success, since the entire institution operates outside U.S. civil and criminal law in most respects.
How about a senior officer in Hasan’s chain being subpoenaed by the Senate Armed Services Committee (under new management) & being asked,
“General, you knew this officer posed a risk to those around him by his espousal of radical Islam through his public statements & his membership in a jihadi mosque.”
“Please explain to this committee why nothing was done to evaluate what turned out to be a lethal threat.”
It’s not a civil suit, got it. But it’s entirely possible that a Congressional inquiry could result in someone getting court-martialed for dereliction or negligence. By those in the chain who don’t want to wind up in the same boat.
That would help to provide some closure for the family members, IMO.