"The wrath of God is not declared against unrepentant sinners merely because of the sins they have committed, but because, when called to repent, they choose to continue in resistance, repeating the sins of the past in defiance of the light given them. If the Jewish leaders had submitted to the convicting power of the Holy Spirit, they would have been pardoned; but they were determined not to yield. In the same way, the sinner, by continued resistance, places himself where the Holy Spirit cannot influence him. AA 62.1"
"For it is impossible for those who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost, And have tasted the good word of God, and the powers of the world to come, If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame."
Both passages discuss the consequences of resisting the Holy Spirit and the possibility of reaching a point where repentance becomes difficult or impossible. The Hebrews passage is a warning, while the EGW passage explains how this state is reached through continued resistance.
"On the day following the healing of the cripple, Annas and Caiaphas, with the other dignitaries of the temple, met together for the trial, and the prisoners were brought before them. In that very room and before some of those very men, Peter had shamefully denied his Lord. This came distinctly to his mind as he appeared for his own trial. He now had an opportunity of redeeming his cowardice. AA 62.2"
"Then took they him, and led him, and brought him into the high priest’s house. And Peter followed afar off. And when they had kindled a fire in the midst of the hall, and were set down together, Peter sat down among them. But a certain maid beheld him as he sat by the fire, and earnestly looked upon him, and said, This man was also with him. And he denied him, saying, Woman, I know him not. And after a little while another saw him, and said, Thou art also of them. And Peter said, Man, I am not. And about the space of one hour after another confidently affirmed, saying, Of a truth this fellow also was with him: for he is a Galilean. And Peter said, Man, I know not what thou sayest. And immediately, while he yet spake, the cock crew. And the Lord turned, and looked upon Peter. And Peter remembered the word of the Lord, how he had said unto him, Before the cock crow, thou shalt deny me thrice. And Peter went out, and wept bitterly."
The EGW passage explicitly refers to Peter's denial of Christ and his opportunity to redeem himself before the same people. This is a clear and direct allusion to the events described in Luke 22:54-62.
"Those present who remembered the part that Peter had acted at the trial of his Master, flattered themselves that he could now be intimidated by the threat of imprisonment and death. But the Peter who denied Christ in the hour of His greatest need was impulsive and self-confident, differing widely from the Peter who was brought before the Sanhedrin for examination. Since his fall he had been converted. He was no longer proud and boastful, but modest and self-distrustful. He was filled with the Holy Spirit, and by the help of this power he was resolved to remove the stain of his apostasy by honoring the name he had once disowned. AA 62.3"
"But I have prayed for thee, that thy faith fail not: and when thou art converted, strengthen thy brethren."
The EGW passage directly references Peter's conversion and how it strengthened him, echoing the sentiment in Luke 22:32. The passage amplifies the idea of Peter's transformation after his denial of Christ, which is directly linked to the prayer Jesus offered for him.