Tested under controlled conditions, intercessory prayer fails.
The objection, in full
The 2006 STEP study (Templeton-funded, ten years, 1,800 cardiac patients) found no benefit from intercessory prayer — and a slight negative effect for those who knew they were prayed for. Amputees never regrow limbs. Catholic and Protestant child mortality rates track local medicine, not local devotion. If prayer is real communication with an omnipotent friend, the silence on the line is deafening.
The proper, if somewhat ungainly, formulation is: those who knew they were being prayed for had a slightly higher rate of complications.
or, in plain terms —If prayer worked, amputees would grow limbs back. They don't.
Prayer is not a vending machine.
The objection imagines prayer as a system of inputs and outputs: enough prayers in, the desired outcome out. On this model, of course prayer "fails." It would also fail as a model of friendship, or marriage, or any relation between persons. You do not summon your wife by repeating her name with sufficient sincerity. She is not a vending machine, and neither is God.
Prayer in the Christian tradition is not primarily a mechanism for getting things. It is the alignment of the creature with the Creator — a participation in the divine will, not a manipulation of it. Thy will be done is the model, not an afterthought. When Jesus prays in Gethsemane, he asks; he is refused; he submits. This is the pattern.
That said, prayers are answered. I have seen them answered. But the answer comes on God's terms and his timing, and is often not what was asked. Asked for relief, we are sometimes given strength to bear. Asked for the dead to be raised, we are sometimes given the courage to bury them.