This world is for deeds with recompense not necessarily being tied to one's deeds, while the hereafter is a world of recompense and no deeds. The 6419th hadith in Sahih al-Bukhari does not mean that once one reaches 60 years of age, one's repentence will not be accepted; rather, it means that one may not be excused if one claims that one did not have enought time to repent. From Qur'an 35:37, the wrongdoers will acknowledge their mistakes and will acknowledge that the hereafter is not a place of deeds. They will accordingly ask to be returned to this world so that they can do the the righteous deeds. Allah's response to them is that they were indeed given ample time time during their lives:
وَهُمْ يَصْطَرِخُونَ فِيهَا رَبَّنَا أَخْرِجْنَا نَعْمَلْ صَالِحًا غَيْرَ الَّذِي كُنَّا نَعْمَلُ أَوَلَمْ نُعَمِّرْكُم مَّا يَتَذَكَّرُ فِيهِ مَن تَذَكَّرَ وَجَاءَكُمُ النَّذِيرُ ۖ فَذُوقُوا فَمَا لِلظَّالِمِينَ مِن نَّصِيرٍ
And they will cry out therein, "Our Lord, remove us; we will do righteousness — other than what we were doing!" But did We not grant you life enough for whoever would remember therein to remember, and the warner had come to you? So taste [the punishment], for there is not for the wrongdoers any helper.
— Surat Fatir 35:37
This hadith does not necessarily define "enough" in the verse above as being 60 years, but states that 60 years is beyond that age where people are considered to have had "enough for whoever would remember therein to remember".
In Fat'h Al-Bari 11/239-240, Imam Ibn Hajar al-'Asqalani explained that there is no exact age beyond which one is considered to have had ample time to repent. Most scholars agree that it is the age of maturity, but some consider the age of maturity to be 40 years (e.g., Masrūq, At-Tabari), 46 years (e.g., Ibn 'Abbas, Ibn Mardawaih), 60 years (e.g., 'Umar, Abu Huraira).
In the end, forgiveness comes only from Allah, and the hadith does not restrict Allah's forgiveness to those who are younger than 60 years of age; rather, it states that those who have completed 60 years of age will be given the response in Qur'an 35:37 that they had enought time to repent during their lifetime.