Should heart stimulants be administered to a child born with brain damage due to lack of oxygen, who is in a complete coma, knowing that doctors believe his condition is hopeless and that he would live a life of torment in bed if he survives?

If stopping the child's heart stimulants will lead to his death, then this is considered causing his death, which is forbidden (haram). One must not despair of Allah's mercy, and Allah knows best the child's condition and His wisdom in His creation. The discontinuation of the heart stimulants for the child must be refused, and the doctor bears responsibility if he does so.