This was posted by a friend of mine on CARM's charismatic forum. He uses the moniker "Beaker". I thought you might enjoy his insights:
1. Miracles follow the preaching of the gospel
Mark 16:15-18 makes it clear that the healing of the sick accompanies the going into the entire world. Because the gospel is reaching the lost, God performs "signs and wonders" (which include but are not limited to healings) to get their attention. If you're not reaching the lost, you aren't "going," so why should you expect any signs to follow you? God confirms his Word. If you aren't giving out his Word, there is nothing for him to confirm! On the mission field, there is a greater emphasis on evangelism, so there would tend to be more dramatic confirmations of the gospel message.
2. They don't have Christian bookstores full of anti-healing unbelief books
It's great to tell new believers what they have in Christ before the wet-blanket crowd gets a chance to tell them that you never know what our sovereign God will do, Paul had an eye disease, and you're Job II. Once people latch on to these arguments, you cannot get them healed unless you can show them why these arguments are invalid.
3. They have a greater desperation for miracles because the medical facilities aren't as good
People in most countries can't just show a card and get medical treatment for most conditions. Many times, either God heals them or they don't get healed at all. Thus, they are more desperate for miracles. They are like the woman with the issue of blood who spent all her living on doctors, but only grew worse. She was so desperate that she risked execution for being in public to get her healing. People who are that desperate are ripe to receive a miracle. If you can live with your illness because you can get some medicine at the local drugstore, you probably will live with it instead of without it. You aren't desperate enough.
However, desperation by itself is not faith, and "desperate" prayers don't work unless they are desperate faith prayers. Remember, the woman in Mark 5 was desperate, but she came in faith based on what she had heard of Jesus. She was not coming in desperation alone. The people need to hear God's healing covenant so that they can pray in faith, not simply in desperation.
4. They don't intellectualize everything
Education is good, but it makes a lousy god. You can't completely grasp the things of God with your head. Faith is of the heart. Jesus never told you to believe in your head. Sometimes we block our healing by trying to intellectualize it instead of believing it in our hearts. It's good to educate your head, but not at the expense of growing in the things of the Spirit. People overseas are often less educated and would be less likely to have this problem.
5. God meets people where they are
People on the mission field are often more open to the gifts of the Spirit. They may not know much about the Word, but they know that God can do miracles. They are much like the nobleman in John 4:46-53. They are unlearned, but also tenacious and sometimes desperate to see miracles. God is willing to meet them where they are. His perfect will is for them to know the truth so that they do not have to depend on manifestations of the Spirit for healing. But God knows that they have not had the opportunities you have to hear the Word taught, and he is patient with them.
6. They are used to the supernatural
The devil is happy to move wherever he has an open door, and less-developed countries often have more demonic activity than more-developed countries. The people already know that there is a spirit realm and that the supernatural is real. Witch doctors still make a good living in many places by "healing" the sick temporarily until the devil feels like making them sick again so that they have to go pay the witch doctor more money. I think it is easier for the people to accept the supernatural side of the gospel when they are used to the supernatural in general.
1. Miracles follow the preaching of the gospel
Mark 16:15-18 makes it clear that the healing of the sick accompanies the going into the entire world. Because the gospel is reaching the lost, God performs "signs and wonders" (which include but are not limited to healings) to get their attention. If you're not reaching the lost, you aren't "going," so why should you expect any signs to follow you? God confirms his Word. If you aren't giving out his Word, there is nothing for him to confirm! On the mission field, there is a greater emphasis on evangelism, so there would tend to be more dramatic confirmations of the gospel message.
2. They don't have Christian bookstores full of anti-healing unbelief books
It's great to tell new believers what they have in Christ before the wet-blanket crowd gets a chance to tell them that you never know what our sovereign God will do, Paul had an eye disease, and you're Job II. Once people latch on to these arguments, you cannot get them healed unless you can show them why these arguments are invalid.
3. They have a greater desperation for miracles because the medical facilities aren't as good
People in most countries can't just show a card and get medical treatment for most conditions. Many times, either God heals them or they don't get healed at all. Thus, they are more desperate for miracles. They are like the woman with the issue of blood who spent all her living on doctors, but only grew worse. She was so desperate that she risked execution for being in public to get her healing. People who are that desperate are ripe to receive a miracle. If you can live with your illness because you can get some medicine at the local drugstore, you probably will live with it instead of without it. You aren't desperate enough.
However, desperation by itself is not faith, and "desperate" prayers don't work unless they are desperate faith prayers. Remember, the woman in Mark 5 was desperate, but she came in faith based on what she had heard of Jesus. She was not coming in desperation alone. The people need to hear God's healing covenant so that they can pray in faith, not simply in desperation.
4. They don't intellectualize everything
Education is good, but it makes a lousy god. You can't completely grasp the things of God with your head. Faith is of the heart. Jesus never told you to believe in your head. Sometimes we block our healing by trying to intellectualize it instead of believing it in our hearts. It's good to educate your head, but not at the expense of growing in the things of the Spirit. People overseas are often less educated and would be less likely to have this problem.
5. God meets people where they are
People on the mission field are often more open to the gifts of the Spirit. They may not know much about the Word, but they know that God can do miracles. They are much like the nobleman in John 4:46-53. They are unlearned, but also tenacious and sometimes desperate to see miracles. God is willing to meet them where they are. His perfect will is for them to know the truth so that they do not have to depend on manifestations of the Spirit for healing. But God knows that they have not had the opportunities you have to hear the Word taught, and he is patient with them.
6. They are used to the supernatural
The devil is happy to move wherever he has an open door, and less-developed countries often have more demonic activity than more-developed countries. The people already know that there is a spirit realm and that the supernatural is real. Witch doctors still make a good living in many places by "healing" the sick temporarily until the devil feels like making them sick again so that they have to go pay the witch doctor more money. I think it is easier for the people to accept the supernatural side of the gospel when they are used to the supernatural in general.
When I read the book "I Just Saw Jesus" by Paul Eschelman with Campus Crusade for Christ, he pointed out some of the same things. CCC is not known for the supernatural happening in their meetings but they were most definately encounterd in other countries. One story I remember was when they had the Jesus Film showing in the middle of the jungle, on bedsheets hung from one tree to the next. I don't remember what country, but the people watching, believed what they saw Jesus doing on the screen, called out to Him and they were healed right there.
The young girl, frightened at first, relaxed at the gentleness of the woman. After the prayer they hugged and that was the extent of their contact. However, by the time the young girl got to the bus to go back to the hotel. . .she looked down at her hands and they were totally clear of any bites. There was not even a trace of bites. 
