"neglect him" is correct and usable in written English.
You would typically use it when referring to someone's lack of care or attention. For example, "My father neglected me for most of my childhood."
The major orchestras and record companies began to neglect him, as did the Proms.
Eventually, but unsurprisingly, the great medieval monasteries that preserved classical texts by patient copying of manuscripts came to neglect him.
And his happiness seems to him to be in turn undermined by the forgetfulness of his patron, Charles II, who will sometimes desire his company, and then for years neglect him.
Do not pay him homage in the temple clad in silk, only then to neglect him outside where he is cold and ill-clad.
Tommy's parents begin to neglect him; he is tortured by his sadistic "Cousin Kevin", and molested by his uncle Ernie ("Do You Think It's Alright?", "Fiddle About"), and given LSD by the Hawker's wife, "The Acid Queen".
His alcoholic father neglected him.
Johnny, meanwhile, feels that his father has been neglecting him.
They expected him to be perfect, but they neglected him.
She feels guilty, and says she's neglected him.
They owed him a duty of care and they just neglected him.
