24-7 Prayer vigils have always been used powerfully by God:
2000 years ago the church was born in a 24-7 prayer room.
2020 Vision, 24-7 Prayer, p 6
This seems to be something these 24-7 Prayer people seem to hold on to and believe. But is it true?
12Then returned they unto Jerusalem from the mount called Olivet, which is nigh unto Jerusalem, a Sabbath day’s journey off. 13And when they were come in, they went up into the upper chamber, where they were abiding; both Peter and John and James and Andrew, Philip and Thomas, Bartholomew and Matthew, James the son of Alphaeus, and Simon the Zealot, and Judas the son of James. 14These all with one accord continued stedfastly in prayer, with the women, and Mary the mother of Jesus, and with his brethren.
Now, this passage does say that they were steadfast in prayer. But it doesn't say that they established some kind of all-day-and-night prayer vigil, or what have you. Furthermore, Christ had already promised that the Spirit was coming to them, before they entered this upper chamber and began waiting and praying.
1000 years ago Celtic monasteries prayed 24-7 and transformed Europe.
300 years ago Moravians prayed 24-7 for 100 years and took the gospel to many nations.
104 years ago a multi-racial 24-7 Prayer Room on Azusa Street in Los Angeles sparked the global Pentecostal and charismatic renewals.
I can't claim to know much about Celtic monasteries and Moravians, so I'll leave that be. But I'm kind of caught in a curious spot in regards to the charismania of today. On the one hand, I simply haven't found a good biblically-based argument against the spiritual gifts like tongues still being for today. The Bible does not explicitly say that it will end when John finishes the Revelation of Jesus Christ.
On the other hand, given how far too many of the leaders in the various forms of the charismatic churches are mindlessly following the words of charlatans, false prophets, false healers, false apostles, televangelists who preach more of people fulfilling their own desires than repentence and faith in Christ, I would contend that what came from Azusa Street has at least been perverted to an incredible degree, to the point even where too many in the charismatic churches, especially the leaders, are actively against God, even as they blasphemously use the names of God and Jesus to give their bizarre and false teachings a thin veil of legitimacy.
So, simply linking what their doing to Azusa Street may not mean much.
Finally, we simply have this plain fact--nowhere in the New Testament is any church commanded to set up some kind of all-day-and-all-night prayer thingy. Paul never mentions such a thing in any of his letters, the epistles of James and Peter and John are resoundingly silent on such a practice, and Jesus Himself doesn't mention the supposed need for it. There is nowhere any promise that if the churches were to put such a notion into practice, they would be blessed and their churches would grow and they would be cool.
So, I would contend that the notion that God has used such things powerfully is a bit of a stretch.