All prayers are always answered
If you make problems real, your prayer is "I want this problem", and so it is given you. Your prayer is answered. Even if in words it seems your prayer is "I do not want this problem", your actual prayer is that you do.
When your prayer is sincerely not focusing on "I have this real problem" and is instead truly acknowledging the perfection of God, God's perfection will be what you are asking for, and God's perfection will be what you are given.
This is what the whole "Song of Prayer" pamphlet for ACIM is about. It's telling us to sing a higher song. To express the basic prayer "this is what's true for me", which is more of an expression of affirmation or acknowledgement, than it is a question. And that's because there are no real questions, only assertions.
So whatever you are asserting, that is what you are expressing as what you want and believe in, and that is what you will get.
So if you assert and acknowledge the truth of God and the presence of divine health and perfection and happiness, that is what God will happily share with you, and will move mountains that you would have it to extend to others.
God does not fail to "answer prayers". It is YOU who decides what you will give to yourself. God is ALWAYS providing the fullest love, and when your prayer is actually saying "I don't really want love" God is honoring that, to honor your free will.
This is the true meaning of "God helps those who help themselves." - you must be willing to be PART OF the atonement, to be the GIVER of the miracle that you would receive, to position yourself seeing things with God's eyes, not through the ego's eyes. To acknowledge and be grateful for the abundance of God's blessing. If you are not willing to participate in the extending of love, how can you receive it?
God is always fully giving. Fully giving is creation. It is sharing. It is how God created souls and made each of them complete and full in and of themselves, endowed with completely free will, because they are given fully as expressions of unconditional love and freedom.
If prayers seem broken or not heard, you are not asking for what you think you are asking for, and so you are in fact receiving more of what you are actually asking for, and thinking it is not what you asked for. Ego must be let go and out of the way in order to "accurately" pray and have your receiving line up with your expressing.
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