Did you ever consider that when you are delivered from trouble that it is not necessarily for your benefit? Could it possibly be something greater at work than your immediate help or cure that helps comes from God?
"But, Doug, that's crazy talk! Of course it is for me!" Sure it is. But is it all for you and because of you? That is the topic of consideration.
Think of the sickness and subsequent death of Lazarus. (John 11:1-44) Jesus, on hearing that Lazarus was sick told His disciples, "This sickness will not end in death. No, it is for God's glory that God's Son may be glorified." (vs. 4) And then when Lazarus DID die, and when Jesus arrived and prepared to raise him from the dead He prayed, "Father, I thank you that you have heard me. I knew that you always hear me, but I said this for the benefit of the people standing here, that they may believe that you sent me." (vs. 41-42) You see, Lazarus death and then Jesus raising him from the death was all to bring glory to God.
"Help us, O God our Savior,
for the glory of your name;
deliver us and forgive us our sins
for your name's sake."
Our deliverance is for our benefit, but more than that it is for God's glory. He who was able to raise Lazarus from the dead, is able to forgive and bring deliverance to this wretched man, and there is nothing that He cannot do to bring glory to Himself and His name.
So the next time you ask God to save you from the predicament you find yourself in, remember it is for your benefit AND His glory that He brings you out of a place from which you could never save yourself. And because of that He will draw others to Him.