In my experience, both from living and from reading the Bible, there are two reasons why God may not help us right away when we're suffering:
1. We're being punished for the sins we've committed after being saved. God lovingly disciplines His children, so that they will not continue to sin against Him.
2. God is trying to bring glory to Himself in some way. This could mean something like drawing you closer to Him or showing that He has power over tough situations. The Bible says that He has purposely given people physical ailments, just so that He can bring Himself glory by healing them later. People tend to appriciate being healed more than being born healthy in the first place.
While God may not help you if one of these two situations applies, there are many instances where He will heal you. If you're going through a tough time, and you place your faith in the Lord for deliverance, He just may decide to help you.
"Jesus replied, "I tell you the truth, if you have faith and do not doubt, not only can you do what was done to the fig tree, but also you can say to this mountain, 'Go, throw yourself into the sea,' and it will be done. If you believe, you will receive whatever you ask for in prayer."
Matthew 21:21-22
"Ask and it will be given to you; seek and you will find; knock and the door will be opened to you. For everyone who asks receives; he who seeks finds; and to him who knocks, the door will be opened. Which of you, if his son asks for bread, will give him a stone? Or if he asks for a fish, will give him a snake? If you, then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give good gifts to those who ask him! So in everything, do to others what you would have them do to you, for this sums up the Law and the Prophets."
Matthew 7:7-12
"Have[a] faith in God," Jesus answered. "I tell you the truth, if anyone says to this mountain, 'Go, throw yourself into the sea,' and does not doubt in his heart but believes that what he says will happen, it will be done for him. Therefore I tell you, whatever you ask for in prayer, believe that you have received it, and it will be yours. And when you stand praying, if you hold anything against anyone, forgive him, so that your Father in heaven may forgive you your sins."
Mark 11:22-25
"Then he said to them, "Suppose one of you has a friend, and he goes to him at midnight and says, 'Friend, lend me three loaves of bread, 6because a friend of mine on a journey has come to me, and I have nothing to set before him.' Then the one inside answers, 'Don't bother me. The door is already locked, and my children are with me in bed. I can't get up and give you anything.' I tell you, though he will not get up and give him the bread because he is his friend, yet because of the man's boldness[e] he will get up and give him as much as he needs. So I say to you: Ask and it will be given to you; seek and you will find; knock and the door will be opened to you. For everyone who asks receives; he who seeks finds; and to him who knocks, the door will be opened. Which of you fathers, if your son asks for[f] a fish, will give him a snake instead? Or if he asks for an egg, will give him a scorpion? If you then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give the Holy Spirit to those who ask him!"
Luke 11:5-12
We are cautioned about our motives when asking for something in this last verse.
You want something but don't get it. You kill and covet, but you cannot have what you want. You quarrel and fight. You do not have, because you do not ask God. When you ask, you do not receive, because you ask with wrong motives, that you may spend what you get on your pleasures.
James 4:2-3