Sayyiduna Abu al-Darda' (may Allah be pleased with him) says: People mentioned kinship in the presence of the Prophet (peace and blessings be upon him). We said: "Does the life of one who maintains the ties of kinship become longer?" The Prophet (peace and blessings be upon him) said: "There is no increase in lifespan, for Allah Almighty has said: 'When their appointed time comes, they cannot delay it by a single hour, nor can they bring it forward.' Rather, what is meant is that a man has righteous offspring who keep supplicating for him after he is gone, and the reward of that keeps reaching him; so it is as if his life had been increased."
Al-Tabarani recorded it in al-Mu'jam al-Saghir and al-Mu'jam al-Awsat. There is no matruk (abandoned) narrator in its chain, but they have been declared da'if (weak).