Sometimes when we are praying for a particular thing, we need to be like a dog with a bone. And sometimes we need to relinquish. How do we know when to persevere and when to let go?
I regularly need to remind myself that there are no formulas that can help me figure this out. That is why we must invite the Holy Spirit into our confusion and trust Him to show us the way.
If you have discerned that God is very pleased with what you are asking for in prayer- that is, you realize that it is consistent with the person, teaching, life and ministry of Jesus (who is the personification of God's will and nature), then you have every reason to be confident that God wants you to have what you are praying for (see 1 John 5:14,15). It is likely that though you ask in keeping with His will, you may not see the answer materialize immediately. This is common, as there is usually a gestation period between the conception of a request and the birth that is the answer. Many beautiful souls have discovered the art of persevering prayer and they have learned to stand firm.
On the other hand, it may be that the very good thing we are praying for, a thing that God actually wills to give us has become an idol to us. Perhaps we have somehow deemed it essential to our very survival. This situation will act as a block to our prayers.
For this reason, we need to discern whether the Spirit is guiding us to hang on or let go. Thank God, He will show us. Simply ask Him to make it clear.