Does neurogenic stuttering ever just randomly all of a sudden stop occurring after a stroke?

Most likely not. It depends on the site of the stroke as to how severe the stutter will be. Because the stutter is a result of injured brain sites which control important nerves and brain connections, unless these lesions healed to a state that speech motor mechanisms could become fully functional again, the stutter would most likely remain to some degree. As the brain heals the stutter may improve, but like you said, it does require intensive therapy.