Does prayer work at a distance?
Well, of course it does. Based on the centurion's faith, his servant was healed at a distance in Matt 8:5-13 and Luke 7:1-10. Based on the faith of the Syrophoenician woman, her daughter was delivered at a distance in Matt 15:21-28 and Mark 7:24-30. Based on the faith of Jesus, the royal official's son in Capernaum was healed at a distance in John 4:46-54.
Note that of the three examples above, only one case, the third case, was of Jesus healing at a distance. In the first case, Jesus said to the centurion, "I will go and heal him," but the centurion stopped him. In the second case, Jesus refused to heal the woman's daughter. In both of those cases, Jesus commended each of them as having "great faith."
That third case could also be one of Jesus simply not wanting to go again into the city of Capernaum to heal someone. We know from John 2:12 that Jesus had already been to Capernaum. In Matt 11:23 and Luke 10:15, Capernaum was one of the cities that he denounced, because they did not repent after seeing the miracles performed there. A similar situation can be seen with Bethsaida, a city that he likewise denounced. He visited Bethsaida starting in Mark 6:45, healed many people, and left the region in Mark 7:24. When he went there again in Mark 8:22 and found a blind man, he first led him out of the city before healing him.
You can see from this that, in the time of Jesus, "healing at a distance" was very rare, and had to do with extenuating circumstances, if we use all the accounts of healings in the gospels as statistics, for Jesus himself is recorded as healing at a distance only one time.
In the rest of the New Testament (Acts and epistles), it is the same. In fact, there is the case of Timothy having some kind of stomach problem, and the apostle Paul, at a distance, recommends to him by letter that he stop drinking only water and take a little wine for it, in 1 Tim 5:23.
By contrast, in modern churchendom "distance prayers" are the norm, with people receiving prayer requests and offering prayers in church or other group meetings, receiving and offering prayers via computer over the internet by e-mail, instant messaging, social networking, and/or then going to their "prayer closets," so to speak, to do "warfare." There is usually very little effort, if at all, to reach out to people in person, face to face.
Granted, there must be some consideration that, given today's information technology, a situation could easily be outside of physical reach, whereas in the time of Jesus, information about a situation came from a place that was not farther than one could travel by foot, and there was no timely information beyond that distance.
However, there is now prevalent somewhat of a non-contact mentality, which is just for personal convenience and therefore amounts to laziness and lack of resolve. I've observed that the effectiveness of people in these scenarios is generally dismal.
As Jesus got as close as he could to people, we should too. There is another important aspect to this, and that is that there is usually more to the situation than just a specific problem needing to be remedied as the object of a specific prayer. Jesus commissioned us to make disciples, not just fix specific problems that need to be remedied. Interaction with the person who is the object of prayer is necessary to do this, and that can most effectively be done face to face. Additionally, there are often others in the company of the person of interest when doing so who also would benefit from personal ministry to them, who also may have problems to be addressed and remedied as well, and who could also be discipled.
I grant this work to the public domain.