First of all, there ARE amputees getting their arms and legs back, it happens pretty frequently actually. You just don't see them in the States so much because it is a bit harder to believe for something like that to happen, than for pain you can't see to go away. People all around the world are getting whole new body parts, new lungs, hearts, even brains. So, thinking that it is just low key stuff, that's just from a lack of field experience.
Second, there are three reasons why healing can take time. First it could be that when a person first starts trying to get people healed, they don't really understand how healing works, and it takes time to learn so it can happen.
Second, the law of sowing and reaping is very valid today and not just with finances unlike what some people may have you believe. It is the same with healing, if you sow healing through prayers, eventually you will start to reap healing through the manifestation of it. It takes a bit of time to grow.
Third, the other reason could be a situation like Daniel's fast. He decided to seek God, and the Bible says that the answer didn't show up for 21 days because there were demonic forces holding back the answer. Many times you can pray for someone to get healed, and the devil resists, and tries to delay it. It turns into a staring contest so to speak, the problem is that in North America you guys live in a microwave society and want everything instantly and don't want to be patient, you definitely don't want to wait 21 days or a month or more for something to happen. SO, you back down and give up deciding that it wasn't the will of God for that person to be healed, when in fact it ALWAYS is the will of God for healing, but there is spiritual warfare involved and if you stay firm it will absolutely happen.
So that's why. There could be other factors like sin in the life of the person praying and so on, but in the end, those are the basics.
Alan
http://www.newheightsministries.net