Can Satan (or demons) be bound by believers under authority given by God?
Absolutely not. Again, when some Christians claim to bind Satan in their prayers they are employing a faulty hermeneutic. Such binding has not yet taken place—it will take place at the beginning of the millennial reign of Christ. The devil will be bound for a 1000 years. One of the inconsistencies of some Pentecostal theology (from which quarter this kind of statement/activity tends to come) is that they tend to pick and choose whatever seems to be sensational even if it wreaks havoc to their theological system. They tend to be dispensational and pretribulational—a viewpoint which necessarily makes them premillennial. And if premillennial, then they must believe that the binding of Satan does not occur until Christ establishes his kingdom on earth. There are two points here of significance: (1) the binding will not take place yet; and (2) Christ and Christ alone will bind Satan.
So, in summary, I’d say that the error of these charismatics is twofold: (1) a faulty hermeneutic which has no consistency, but is essentially sensationalistic; (2) an anthropocentric focus in which God may well be viewed as powerful, but he is still viewed as impersonal—thus, God becomes the instrument that the almighty Christian wields!
The error of a number of non-charismatics too often is that though they see the greatest miracle of all occurring all the time—the raising of the spiritually dead—they often fail to believe that God will do lesser works among them. However, those who have been or are now in a crisis often come to embrace a more holistic understanding of God’s grace and power in their lives.
May God give all of us wisdom and grace to discern our own errors and to grow in knowledge and application. May He also help us to graciously share the blind spots of others with them as brothers and sisters in Christ.
For a further discussion of Spiritual Warfare see: Bob Deffinbaugh's article - "Spiritual Warfare (Ephesians 6:10-20)", and Charles Buntin's article - "Appendix 1 The Holy War--A Spiritual Warfare Primer".
For a further discussion of Satan, his role, and God's plan see: Bob Deffinbaugh's article - "Satan's Part in God's Perfect Plan"
Related Topics: Satanology