That prayer stands out as it shows us their understanding and application of the doctrine of the sovereignty of God, amongst other things. As they face persecution they believe that God is sovereign, that he works even the opposition of evil people to his purposes, that is just how sovereign he is. They apply that doctrine and pray that persecution would not lead them to be silent.
It's the same in chapter 8 as they respond to the persecution led by Saul that scatters the church. Behind the scenes we see that God is sovereign even over Saul's actions. What is Saul's aim? He will stop at nothing short of the destruction of the church, he wants the church either imprisoned, or scared into silence or scattered and isolated so that Jesus name fades away into history. But God is sovereign, so sovereign that Saul's opposition only leads to the advancement of God's mission, the spread of the name and work and wonder of Jesus Christ and the knowledge of the salvation that is found in his name alone. Saul's attempts at stamping it out only serve to spread it.
This image has been stuck in my head as I've read this passage over and over again. A gardener will pull up dandelions to stop them spreading. Now imagine that gardener is a young dad weeding the dandelions whilst his children play. Unbeknown to him as he piles up the uprooted dandelions behind him the children are picking them up and blowing on them dispersing the dandelion clocks all over the garden.
That is something of the image here. Saul is trying to uproot and destroy the church and it's as if our Sovereign Father is behind him just blowing his seed through his people all over Judea and Samaria. God's gospel will flourish whilst God remains sovereign even when it looks as if persecution signals the end of the church. What an encouragement as we look at our world where Christians are persecuted in the Middle East, as many of our brothers and sisters have to flee their homes. They go carrying the gospel with them, let us pray that they are not cowed or silenced but boldly witness of their, and our, Saviour and that God's kingdom comes. What an encouragement as hostility to the true gospel increases in our own nation, God is sovereign and we can stand.