The atheist, in my opinion, has arrogantly challenged God by viewing non-answered prayer as evidence that he does not exist. The Bible says that God hides himself from the proud (James 4:6). So, according to Scripture, the atheist cannot and will not see that prayer works.
Atheists are often very aggressive when it comes to attacking Christianity and one of the topics they often criticize is prayer. Since they believe (deny, lack belief, etc.) that there is no God, therefore prayer cannot work -- no matter what is said. The problem is that atheists who attack Christianity on this level are woefully ignorant of their own false assumptions and hinder their objectivity and they don't understand how prayer works. In the first place, atheists can only assume that God does not exist. They cannot know for sure that God does not exist because it is not possible to know all arguments and evidences for and against God's existence. So, the atheistic position of "no God" is, ultimately, held as a belief.
Second, how would an atheist judge whether or not prayer works? Do they want repeatable experiments and regular quanfiable data? Prayer doesn't work like that. The problem for the atheist is that prayer is offered to a Living Being who has a will and who who, according to Christianity, works all things after the counsel of his will (Ephesians 1:11), not ours. Also, prayer is not a practice where a formula type prayer is uttered and certain results are guaranteed. Instead, God, like any rational being, may or may not answer a request from someone. Think about this. If my child asks me for ice cream and I don't want to give it to her, does it mean I don't exist or that her asking me for things doesn't work?
Third, it seems that atheists want a one-for-one correspondence between prayer requests and results. Otherwise, they say, how can prayer be verified? It seems they want a kind of lab experiment where you utter a certain prayer and certain results manifest. But, if this were the case, such a phenomena would not be a demonstration that God exists. Instead, it would be a demonstration that uttering certain words in certain patterns bring a certains results. It would be like conducting an experiment where results become repeatable. This would imply that a new property of the universe has been discovered and quantified. It would be impersonal, and not personal.
But still. Does prayer work? Yes it does. I've experienced it work in profound ways. But, if I were to offer my experiences of prayers, the atheist would say it's too subjective, not quantifiable. So, we are at an impasse. His requirement of observation, testability, etc., can't affirm or deny prayer's efficacy -- which we cannot provide. So, it isn't possible to win with the atheist when he sets up a criteria that is impossible to satisfy, especially when all answers have to filtered through his atheistic world view which requires that prayer not work.
