There are times when it seems that God is not answering prayer.  Sometimes, this is exactly what is happening--God is not answering prayer.  Sometimes, God is saying, "No."  Sometimes, God is saying, "Wait."  

"We know that God does not listen to sinners.  He listens to the godly man who does His will." John 9:31

"Jehovah 's Hand is not shortened, that It cannot save; neither His ear heavy, that it cannot hear: But your iniquities have separated between you and your God, and your sins have hidden His Face from you, that He will not hear.:  Isaiah 59:1

We can pray in the wrong way.  We can pray for the wrong things.  We can pray in the right way for the right things but with unrepented sin in our lives.  

• Lack of faith or rationalized faith is probably the cause of lack of healing in many cases.  It certainly is emphasized in God's word. 
  
• We all have many things in our lives that hinder our prayers.
• The Church is, as yet, very immature.
• We do not seek God in everything.
• We often expose ourselves to things that harden our hearts.
• We get angry with each other and fail to discern the Body of Christ (reality).
• There is an immense spiritual war going on with many battles. 
  
• Even when we are fully engaged, we are sometimes deceived.
• Paul was hindered by Satan.  (1 Thessalonians 2:18)  There is a war going on.  We don't win every battle.that he will not hear."  Isaiah 59:1-2

There are times when God listens and says, "No."  He looks at the whole situation with ultimate wisdom realizing that He is doing something far greater than what we could fully understand.  In this present age, there is a time when God brings people back to Himself.  We call that death.  For the believer, it is just a transition from one form of life to another.  
 
Note: The Name of Jesus is seldom understood.  His Name is His very essence.  God never puts a name on anything that does not describe what that person is.  He doesn't falsely label things.  Sometimes, prayers are said with the label on the end of them: "In Jesus Name, Amen."  If this is just words, just a label, with nothing behind those words, then it constitutes taking the Name of Jesus in vain.  We are to do all things in Jesus name.  If you are picking up your socks, you should do it in Jesus Name.  More about praying in the Name of Jesus  

FREE on-line BOOK (a classic): With Christ In the School of Prayer, by Andrew Murray

FREE on-line BOOK (a classic): The Real Faith, by Charles S. Price

FREE on-line BOOK (a classic): The Meaning Of Faith, by Charles S. Price