So what about all of those who apparently can present a proof that their prayers have been answered ? Well... I will not enter here in any kind of discussions and arguments to prove that someone is right or wrong because there is no sense in it. We have had holy wars for at least few thousands of years and still we have no winners or clear evidence of who is right.
But I want to point out here few points of self realizations:
1. People tend to proof that their prayer has been answered while in reality it was an element of coincidence, luck etc. Thus their prayer will not be answered for the 2nd and 3rd time. And if you try to explain it to them they feel offended because apparently you are challenging and offending their god. It is similar when people work hard themselces to get the object of their prayer and later they give the credit to god that he apparently has inspired them, has given them strength, motivation etc.
2. Some events in people's lives has been preprogrammed before they were born and they somehow subconsciously know about it, pray for it and when it happens they go and tell everyone about almighty god answering their prayers. And it is the same here - it will not repeat itself for the 2nd, 3rd, 4th time or it will not manifest itself in life of every other person praying for it. Of course people try to defend their belief in almighty god at all cost and they explain to themselves that they are too sinful and thus they must pray more.
3. This point applies especially to people who have joined the religion for the first time, they have changed their religion and they have learned about prayer to god for the first time and apparently since than, their life has changed. In this situation people don't realize that their sickness or any other problem that they had before joining new religion, has been closely related to their beliefs and once they are starting to build and accept new beliefs, they allow their sickness to disappear or being suppressed deeper. Temporarily they will feel as if their life has changed and it is better but sooner or later their suppressed problems will come to the surface again and usually they will be much stronger ( their sickness will be worse ) or they will have other problems which will be closely related to their new belief system. Thus it is all just illusion and there is no real change in their life.
This is very similar to the change apparently made through hypnosis, NLP, positive affirmation, meditation or even through taking the pill from the doctor. All of these techniques create a "visible" change but in reality it is only covering the core of the problem with extra layers of energy ( suppression of the problem and making it invisible ) but as I said before, eventually it will come to the surface again. It is impossible to run away infinitely from facing the consequences of our creations and taking responsibility for it.