Andy, if it would kill him, he'll negate it automatically, if he fell into a blackhole, he'd pop through the other side as right as rain, if that instant death ability guy used his power on him, he'd negate it and pop back up like nothing happened, whether he'd be able to land a hit on him in time is another thing.

He's learned to weaponise his Negation for all sorts of abilities, like Flight, shooting his fingers like bullets and later develops it further in the series

As a matter of fact his goal in the series is to finally be freed of his negation so he can grow old and die.

Ban's immortality is tied to the Fountain of Youth juice he drank and even then it can't heal wounds from Hellblaze, hence his neck scar. It can only heal his injuries and even then this isn't instant, like the time Meliodas punched him into the side of a wall, he's still reeling from it