There are many reasons that God has to say know to some of your prayers. The most revealing is that you are asking for something that is not best for you. You may be praying for healing but God knows what your future will be if you were to live. He knows that there is much more hardship ahead that He doesn't want you to go through. He says He will take you home with Him rather than allow you to go through this hardship. His answer to healing is "no."
That applies to any thing you can ask. God knows you and all your circumstances. He knows what you will do and what you can do. He knows the effect your life has on others. Many times He wants you to be a witness during a tough time. Tough times grab others' attention. They watch you as you continue to pray and praise the Lord. It makes an impact on them. God loves these other people, too. Therefore, you go through the tough time. You may continue to ask that God remove it but because He also loves those who are watching you His answer is "no."
Your neighbor prays for rain on his lawn but you are praying that it doesn't rain on your daughter's birthday. God will not make it rain exclusively on your neighbor's lawn. This is true for any conflicting prayers. One prayer may be answered positively which excludes the other prayer. The same would be true of two people praying for the one promotion or two people praying for different people to be elected president. Many times the answer to one prayer means that the answer God must give to the other is "no."
I often think of the Garth Brooks song, "Unanswered Prayers." It is a song about a man seeing his ex-girlfriend at a hometown football game. He remembers praying that he would marry this woman when she was his ex. He introduces his wife and looks at this woman and thanks God he didn't marry the wrong one. I realize that many of the things I pray for are not the best for me. God has a better plan. He has my best in mind each time He thinks of me.
Praise God for "no!" It just means something better is ahead.