The powers of evil to prevail, is latter times, yes, but not the gates of hell. Yes, God permitted Satan 100 years, some say 75 years. IMO Satan's time is very short right now. Mass will cease or nearly in hiding for 3 and a half years/tribulations like man has never seen!
I have read many of Cardinal Mannings books and they are very good. I salute him for clarifying definitions of Vatican I Council. It was such a need, for there was and still is, much confusion, as Our Lady said there would be. And confusion makes catholic sense when there is no pope.
Agreed on all of that. The 100 years probably started on June 13, 1929 with Sr. Lucia's Tuy apparition where Our Lady made this small request:
"The moment has come in which God asks the Holy Father to make, in union with all the bishops of the world, the consecration of Russia to My Immaculate Heart, promising to save it by this means. So numerous are the souls which the justice of God condemns for sins committed against Me, that I come to ask for reparation. Sacrifice yourself for this intention and pray."
Note Our Lady says God is angry specifically for sins committed against her, the Virgin Mary. She ask for reparation for those sins against her.
Jesus explains this in another locution:
"My daughter, the motive is simple: there are five ways in which people offend and blaspheme against the Immaculate Heart of Mary:
1. Blasphemies against the Immaculate Conception.
2. Blasphemies against her Perpetual Virginity.
3. Blasphemies against her Divine Maternity and at the same time the refusal to recognize her as the Mother of all mankind.
4. Blasphemies of those who seek openly to foster in the hearts of children indifference or contempt and even hatred for this Immaculate Mother.
5. The offenses of those who directly outrage Her in her holy images.
Here then, My Daughter, is the reason why the Immaculate Heart of Mary [My Mother] causes Me to ask for this little act of reparation and by means of it, moves My mercy to forgive those souls who had the misfortune of offending her. As for you, try without ceasing, with all your prayers and sacrifices, to move Me to mercy toward those poor souls."
So these evils in the world are primarily caused by men and women offending Our Lady, which empowers Satan and angers God. The antidotes are penance and the Rosary.