Eighteen-month-old Harry Studley, who was shot on 1 July, is being treated at Bristol Royal Hospital for Children.
His father Edward Studley said there were positive signs, however, and that Harry was "recovering really well".
He said: "It's going to be a long road to recovery but he's getting there, back to the little boy he was before."
Mr Studley and Harry's mother Amy Allen said they wanted to thank the hospital and air ambulance teams who helped their son.
Miss Allen said: "It's been a hard and emotional time for the family and everyone that's been supporting us."
Jordan Walters, 24, of Bishport Avenue, has admitted causing grievous bodily harm in connection with the shooting in a high-rise block of flats in Hartcliffe, Bristol.
His 23-year-old partner, Emma Horseman, has been charged with aiding or abetting him to inflict GBH and is next due to appear in court in September.
The father of a toddler who was shot in the head with an airgun says he has been warned by doctors his son could be in hospital for months or even years.