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Good evening Father,
Many Popes in the past did not always have an exemplary life consistent with their duty: worldly power, corruption, and much more.
My question is this: wouldn't Peter’s succession have been lost with these popes who, at that time, ascended to the Chair of Saint Peter for pure desire of power and not to take care of souls?
Jesus intended to communicate spiritual and not material power.
I'm waiting for you to enlighten me, thank you and good evening.
Priest's response
Dearest, 
1. the apostolic succession, that is to say the divine power tangibly transmitted through the laying on of hands, is not canceled by bad conduct.
The Apostolic succession is guaranteed by that seal or character that is impressed on the soul at the moment of sacred ordination.
2. This seal or character is indelible.
This seal or character does not make a person holy, but enables him to perform actions that only God can do, such as making Jesus Christ present with his sacrifice on the altar in the celebration of the Mass and the forgiveness of sins.
One can go to Hell even with the power conferred by the apostolic succession.
3. The Church can suspend a person from celebrating the divine mysteries (this is the so-called suspension a divinis that is sometimes inflicted on some priests) but it cannot eliminate from the soul these divine powers that God himself has infused into it.
4. It is similar to the seal or character infused in the sacraments of Baptism and Confirmation. This seal is also indelible.
This seal does not make one immune to sin and the possibility of going to Hell, but it enables a person to participate in the cult of Christian religion and to transform his or her actions into an act of praise to God, of supplication and of forgiveness.
5. The Catechism of the Catholic Church speaks of it in these terms: “The seal is a symbol close to that of anointing. "The Father has set his seal" on Christ and also seals us in him. Because this seal indicates the indelible effect of the anointing with the Holy Spirit in the sacraments of Baptism, Confirmation, and Holy Orders, the image of the seal (sphragis) has been used in some theological traditions to express the indelible "character" imprinted by these three unrepeatable sacraments.” (CCC 698).
6. Again: “The three sacraments of Baptism, Confirmation, and Holy Orders confer, in addition to grace, a sacramental character or "seal" by which the Christian shares in Christ's priesthood and is made a member of the Church according to different states and functions. This configuration to Christ and to the Church, brought about by the Spirit, is indelible, it remains for ever in the Christian as a positive disposition for grace, a promise and guarantee of divine protection, and as a vocation to divine worship and to the service of the Church. Therefore these sacraments can never be repeated.” (CCC 1121).
7. Perhaps it would be useful for some to report what St. Giuseppe Cafasso, spiritual director of St. Giovanni Bosco, said about the priest who finds himself in Hell. 
These are his exact words: “The Gospel refers to the condemnation and damnation of many, of the useless servant, of the bad rich; but only about Judas did the Divine Redeemer utter this terrible judgment: ‘It would have been better for him if he had not been born’ (Mt 26:24). And although this can be true for any damned soul, it is true that it was applied in a specific way by the infallible mouth of Our Lord to an apostle and a sinner. (…).
That said, let's imagine that we are at the gates of Hell and let's ask ourselves this question: who is that damned soul? Whose soul is that one which is there in those flames? This is the soul of a priest! Someone who once wore my robe, and now no longer has it, he is in Hell; someone who once celebrated at the altar, sat in those courts of penance and climbed those pulpits, he has now ceased these functions, is now in Hell... Someone who perhaps was my schoolmate, in seminaries, my friend in my own pastimes, he has been dead for a long time and is in Hell. (…). 
Is it possible that the star that was to shine in the beautiful sky of the militant Church on earth and triumphant in Heaven has fallen into that pool of fire and sulfur already mentioned in the Apocalypse?
Yes, unfortunately “a great star fell from the sky”.
Is it possible that he who held the keys of the abyss in his hands has then fallen himself there and shut himself in? 
Is it possible that he who acted as God on earth, on God’s behalf, dispensing His graces, has now become His enemy, stripped of all authority, disinherited, cast down to below the demons in Hell? 
And this, my brothers, is the essential state of damnation, the formal constituent of Hell for a priest” (Spiritual Exercises to the Clergy, pp. 141-142).
8. Therefore, misconduct does not cause the loss of the power of the Order nor does it interrupt the Apostolic succession.
To acquire this power, the intention is sufficient, even if one wants to use it in a perverse way.
Judas also accepted to be an apostle, and he was one.
I bless you, I wish you a fruitful feast of Corpus Christi and I remember you in my prayers.
Father Angelo