I have read Deadline, Dominion, and just finished Edge of Eternity. I have also read some of Frank Peretti's novels. From both you and Peretti there seems to be the idea that angels are loosed or bound from intercessory action by whether or not saints here pray, or the time spent, intensity,etc. of the saints' praying. This is a neat speculation, but I would like Scripture that specifically indicates this to be the case. Ask, seek, knock are spiritual directives, but the specific tying in of prayer to warfare between angels and demons and how it affects the circumstances of this world I have not grasped from Scripture. Can you enlighten me?
Read Daniel 10 (or start with chapter 9 to get a fuller context). Daniel prays in chapter 9 and in 10:12 an angel appears to Daniel, saying to him, "your words were heard and I have come in response to them." Verse 13 then says "But the prince of the Persian kingdom resisted me twenty-one days. Then Michael, one of the chief princes came to help me, because I was detained..."
So here you have a clear example of an angel being sent by God in response to the prayers of a saint, and fallen angels ("prince" here is clearly an angel, used for the speaker and for Michael) then detaining him in battle. The answer to prayer is delayed because of this invisible but very real warfare. You also see a territorial nature to demons, as this fallen prince is described as over Persia, a specific country. Presumably he has demons in the hierarchy under his command, spread throughout Persia (as there would not be just one demon assigned to a whole country). Michael, mentioned here, is elsewhere called the archangel, the angelic commander, and the fallen Lucifer, now Satan, would be his counterpart, the commander over fallen angels (demons).
The purity, sincerity or intensity of Daniel's prayer presumably affected the response, as God doesn't hear the prayers of the impure and says "the effectual fervent prayer of a righteous man avails much" (James 5:16). Why then was there a delay in the answer? We don't know, and God is free to delay answers and give us answers we don't like as he wishes, but it seems possible that if others had joined Daniel in his prayer, the righteous angels might have been empowered to resist the demons interfering with their mission. That part is speculation, but the rest seems clear, even if difficult to envision. Best wishes.
For more on spiritual warfare, see Randy Alcorn's book Lord Foulgrin's Letters.