Jesus first told the disciples that all of them would be offended in him that evening and this would be the fulfillment of prophecy (Mark 14:27; cf. Zechariah 13:7), but they didn’t believe him (cf. Mark 14:29). Then Jesus told Peter that Satan has desired (G1809) to sift all the Apostles, as though they were wheat, in order to separate them from Jesus (Luke 22:31). That is, Satan intends to kill Jesus and then scatter the Apostles in hope that he may prove them to be no more than chaff, as he had done with Judas, who, rather than being a disciple of the Lord, proved to be his betrayer.
While it is often assumed that Satan asks God for the right to sift the Apostles, I don’t believe Satan asks God for anything. Neither does he need God’s permission to attack a believer. After all, does a rebel ever ask the permission of his former leader to act out his rebellious deeds? Rather, Satan asks Peter and the other Apostles. He desires them or demands of them—all translations of the Greek (G1809). The word has the sense of demanding for the purpose of trail, according to Strongs Greek Dictionary.
It would be ludicrous to say a thief needs permission from the owner before he could steal his goods. A thief is a thief, because he has no right (permission) to do as he does. Therefore, if Satan is a thief (cf. John 8:44; 10:10), he doesn’t need permission from God to steal or do anything against God’s people. It would be simply out of character of the thief to have to ask permission to do what he does in secret.
In Genesis 3:1 the Serpent came and asked the woman questions that undermined her trust in the word of God. Jesus was quoting scripture and applying it to himself (Mark 14:17; viz. Zechariah 13:7), but neither Peter nor the rest of the Apostles submitted themselves or believed what the word of God clearly prophesied. Therefore, Jesus was able to say through observation that Satan had been already at work demanding of them (Luke 22:31), asking them questions that placed them in the position of unbelief, i.e. instead of trusting Jesus, they were partaking of the Tree of Knowledge and deciding for themselves what was good and what was evil—what was true and what was false.
Jesus told Peter that he prayed for him, assuring him that, in the end, Peter would overcome. The text doesn’t come right out and say it, as it does in 1John 5:15, but it is implied in Luke 22:32 that Jesus’ prayer would be answered. In fact, Jesus, himself, tells us in John 11:41-42 that God always hears Jesus’ prayers.
Once Peter had turned around and repented, Jesus commanded him to establish his brethren. It is possible that Jesus means the other Apostles here, but I think he refers to Peter’s brethren, unbelieving Jews. Jesus was there for 40 days after his resurrection and received eleven of the Apostles back into the inner circle. Therefore, I think Jesus has in mind those who had supported him, but denied him, perhaps were even among those who would cry out to crucify him. These, Peter was told to establish (G4741) in the faith (cf. Acts 3:13-15; 17-19; 1Peter 5:8-10; 2Peter 1:10-12)
Peter responded to Jesus’ words in unbelief. He simply denied what Jesus claimed. Peter simply was not taking into consideration the fact that Jesus quoted scripture (Mark 14:27; Zechariah 13:7). Ordinarily, scripture would be quoted in order to show the certainty of a matter. However, if Peter wouldn’t accept the truth of the scriptures, he was taking the position of an unbeliever. This fact unveils for us the reality that Satan was already at work in sifting both Peter and the other Apostles (Luke 22:31; cf. Matthew 26:35).
In Luke 22:34 Jesus told an unbelieving Peter that before the night was over, he would deny knowing Jesus three times. Nevertheless, while in the state of unbelief, Peter, of course, had to reject Jesus’ statement, as did the other Apostles, who also denied the truth Jesus had been saying (Mark 14:31).