Argument from the inefficacy of prayer
Because prayer is ineffective, skeptics argue that a God who answers prayers cannot exist. This rules out the existence of the Abrahamic god of Judaism, Christianity and Islam. A related argument is that God cannot answer prayers because of his nature or attributes and such a God cannot exist.
- "We pray sincerely, knowing that when God answers this completely heartfelt, unselfish, non-materialistic prayer, it will glorify God and help millions of people in remarkable ways. Will anything happen? No. Of course not. "
Believers sometimes argue the reverse point: prayer is answered and therefore God exists.
- If he exists, God answers intercessionary prayers Mark 11:24
- People pray intercessionary prayers
- Those prayers are not answered or if they are occasionally fulfilled, the outcome is adequately explained by naturalistic causes
- Therefore, such a God does not exist
Apologists attempt to explain why some prayers are apparently answered using a variety of arguments.
Unanswered prayer may serve God's purposes
Another common rationalization is that God uses unanswered prayers to demonstrate his power through the suffering person's life. For example, a patient with terminal cancer whose faith is deepened because of their ordeal. This raises the question, however, of why an all-knowing and all-loving God couldn't think of a less painful way to accomplish that particular goal. It also raises the question of why a person who already had faith has to endure more pain to have it "deepened".
This may explain why God does not intervene in a particular case but does not explain why he never heals amputees.
God does not have to fix your mistakes
A less common rationalization is that a person who gets their leg shot off in a way chose to be on that battlefield of their own free will and, thus, God has no obligation to heal them. However, this ignores the millions born or with missing limbs or caused by accidents that were never healed.
Answered in the afterlife
Some Christians say that Jesus never specified when he would answer prayers and that maybe he will answer them in the afterlife. This is unfair since God apparently answers so many other prayers during the believers' lifetimes. Also, the verses quoted above are unambiguous in the fact that they state that whatever you ask for you'll get during your life.
God should not be put to the test
Others say that God can't be tested since he's so much higher than us. This ignores the story of Gideon in the Old Testament and Thomas in the New Testament who both did exactly that and who received the proof that each had asked for.
As Sagans essay The Dragon In My Garage points out, an untestable God is undistinguishable from a non-existent God.
The verses should be not interpreted literally
Some might bring up the objection that these verses aren't to be taken literally. Firstly, the verses themselves are certainly written like they should be taken literally. Secondly, if this objection is used the believer must provide an objective reason why these verses are non-literal. If no reason can be provided, this claim is special pleading and the verses should continue to be taken literally.
You are not a true believer
Matthew 21:21 says that you must have faith and not doubt for your prayers to be answered. This offers a convenient loophole for unanswered prayers. If you pray and you satisfy every single stipulation and yet your prayer is never answered, Christians can always fall back on saying "You didn't believe enough" or "You doubted your faith". Since there is no empirical way to define how much belief is "enough", this becomes an ad hoc explanation which makes prayer unfalsifiable. It also undermines the fact that some theists will claim that they themselves or people they know of have become believers after being prayed for and where the result was some miraculous event. It is also an example of the No true Scotsman fallacy.
An extension of this argument is that all believers have drifted away from God and he feels under no obligation to respond to prayers.
Prayer and miracles works differently now than in the past
While miracles are common in certain parts of the Bible, they are seemingly uncommon or manifest differently in the modern age.  This is presumed to be part of God's plan. However, no evidence supports this argument and is a form of ad hoc special pleading.
God enables faith by withholding proof
Christians might also say that God doesn't want to provide unambiguous proof of his own existence since this would deny faith. However, this rationalization ignores the myriad of times in the Bible that he does just that.
God does not exist
The conclusion drawn by skeptics is that God does not exist.
- Why Won't God Heal Amputees?
- Proof #44 - Think about a Christian housewife from GodIsImaginary.com: "Take one moment to think about a typical Christian and her "answered prayers.""
- Prayer on An Encyclopedia of Claims, Frauds, and Hoaxes of the Occult and Supernatural (By James Randi)