Don't be so sure that God's silence is His final answer or that it is a "sign" for you to stop asking. If you have done everything right and have made your petition in faith, consider His silence as an invitation to approach Him and talk over the matter a little more. It may be that God wants to see if you are willing to persist in your request and pursue a definitive answer.
I am the Lord, and I created the whole world. 3 Ask me, and I will tell you things that you don’t know and can’t find out. (Jeremiah 33)
7. And shall not God execute vengeance for His elect, who cry out to Him day and night, and patiently watch over them? (Luke 18)
Don't give up until God answers you one way or another. When he does respond it will be one of three answers: Yes, No and Wait.
The answer is YES
Of course, the answer all of us usually want from God regarding our requests is a resounding YES!
Solomon, as a young and inexperienced King of Israel, asked God for something he knew he greatly lacked - wisdom. God responded not only with a loud YES, but gave him far more than he could have dared to ask.
10 The Lord was pleased that Solomon had asked for this, 11 and so he said to him, “Because you have asked for the wisdom to rule justly, instead of long life for yourself or riches or the death of your enemies, 12 I will do what you have asked. I will give you more wisdom and understanding than anyone has ever had before or will ever have again. 13 I will also give you what you have not asked for: all your life you will have wealth and honor, more than that of any other king. (1Kings 3, see also 2Chronicles 1:10-12)
The early church, after Peter was arrested by Herod, offered up fervent prayers for him. What they received from God was nothing short of miraculous. God personally sent one of his angels to free Peter of his chains and escort him out of the prison in which he was held (Acts 12)!
They are, of course, many other examples in scripture where God grants the request of those who pray to him.
The answer is NO
Like it or not, sometimes God's answer to our request is a flat NO. Many times he does not give us what we want because we ask for something to fulfill our own selfish desires and lusts.
3. Then you ask, and you do not receive, because you ask with evil motives, that you may consume it on your own lusts. (James 4:3)
Moses, even though he wanted to enter the promised land with the rest of Israelites, was kept from doing so by God because of his sin. He was only allowed to view Canaan from a distance before he died (Numbers 20:12, Deuteronomy 34:2-5). The apostle Paul wanted a painful affliction taken away from him but was told no. God told Paul that his grace (favor) was sufficient (2Corinthians 12:9). Even Jesus, the son of God, was told NO when he asked that "the cup" of becoming sin for us be taken from him (Matthew 26, see also Matthew 20:22-23).
The answer is WAIT
Having to wait and exercise patience is not easy, especially in a society that expects instant gratification. Yet the character to wait patiently and endure is something God wants in us (Romans 5:1-5).
I waited patiently for the Lord’s help; then he listened to me and heard my cry. (Psalm 40:1)
4 'All right,' I (Jeremiah) answered, 'I will pray to the Lord your God, and I will tell you everything he says.' 7 TEN DAYS LATER, the Lord gave me an answer (Jeremiah 42)
In the final analysis, believers can be confident that their prayers to God do reach him for his loving consideration.
14. And this is the confidence that we have toward Him: that if we ask anything according to His will, He hears us. 15. And if we know that He hears us, whatever we may ask, we know that we have the requests that we have asked of Him (1John 5:14-15)