I had a saying while bow hunting. You can't just shoot them, you're gonna have to kill him. Deer are amazing survivors. Even this buck was walking around after a week with an arrow sticking out of his side. Think about us doing that!
But, in the end, germs and infection set it and likely the bucks stomach was involved. Unable to digest food or eliminate properly he was likely eaten by coyotes once he laid down and couldn't get up.
I've personally witnessed coyotes chasing a buck within a couple hours of being gut shot. They pickup that scent quick.
Sorry, he's dead and probably suffered a slow horrible death while being eaten alive. That's nature.
Deer are more likely to survive a poor gun shot a week after versus and open wound from an arrow that's still in them because at least they have a closed wound with a bullet that has a chance to heal. That arrow ain't coming out.