A person should feel guilty when they do something wrong. You didn't do anything wrong. It serves no purpose here. You know you did, and are doing, the only thing you can do in the face of these horrible circumstances. Save your guilt for when you really need it. Like the next time you flip someone off in traffic only to see that it's a sweet little old lady.
How much harder do you think you should have tried? How many more times should you have told him this disease would kill him? You were fighting a losing battle. You know that. Don't feel guilty that you surrendered. The war was already lost.