There's no reason to doubt that some people here have had multiple experiences of praying for an outcome and then experiencing that outcome. If 10,000 people prayed for things which individually had a 1:10,000 chance of happening, and one of those people experienced the incredibly unlikely thing he prayed for and came on here to tell us about it, we wouldn't know about the 9,999 because people rarely volunteer information about failed prayers (not when they still believe in God, anyway).
Most prayers are probably for things much more likely than 1:10,000, like 1:4 or 1:10. Statistics are not my strong point, but I believe that if someone prays for three things that each have a 1:10 chance of happening, then the total odds of all three being answered are 1:1000. Which means that there's a lot of lucky people out there in a world of billions.
Let's be honest, if we had enough unlikely outcomes after praying about them, or a single once-in-a-lifetime event happened after prayer, like a spontaneous remission of cancer, and this happened at a period in our life where we were searching for answers about what to believe in, there's a very good chance we would be on the other side of the discussion.
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When it comes to faith healing, it's important to remember the power of the mind. Placebo effectiveness on pain is amazingly high and, to start with, a lot of chronic pain is probably psychosomatic. For instance, one might be badly injured in some area; while that area gradually healed, there would be legitimate pain. The brain would then remember that the area is "supposed" to hurt, thus causing the pain to continue until a faith healing one day caused the emotion of wanting to be healed, and then the brain immediately reset its pain memory for that area.
Of course, the faith of a person is likely to be increased by answered prayers much more than it is hindered by unanswered ones. A desire to feel personally special and cared for (even if they "don't know why God answers my prayers and not others") can also be an excellent motivator for a selective bias that causes answered prayers to be remembered and unanswered ones to go unnoticed.