How we define and understand the sovereignty of God are important. If we make an error in this it can lead to a deep sense of hopelessness.
God is indeed sovereign. The Bible shows us that God controls all things. Nothing happens that is outside his divine omnipotence. This wonderful truth ought to give us both hope and peace. It would be an awful and terrifying thing to think of something beyond God's control. If that could happen, then God would not in fact be God at all.
It is easy to cherish the sovereignty of God when things are generally going well in our lives. However, when the trials come (problems related to family, job, money, etc.) doubts may begin to creep in. This is where the danger exists. If we define God's sovereignty as God answering our prayers in the way we want him to, then we are in trouble. This is because God knows much better than we do what we need. We generally desire for God to take away various unpleasant things in our lives. After all, we like comfort. God, however, often uses discomfort to both train us and draw us closer to him.
When God answers differently from what we ask for this does not mean that he has failed to be sovereign. He cannot do that because his sovereignty is one of his unchanging attributes. God applies his sovereignty according to his omniscience. He knows all things, including what is best for us. We are the ones who fail to fully understand how God works out his sovereignty in our lives for his glory. While he may apply it one way, we sometimes think that bad things that happen to us mean God failed in his sovereignty. We are incorrect.
In Romans 8:28 we read, "And we know that for those who love God all things work together for good, for those who are called according to his purpose." God works to bring about what we need, not necessarily what we want. We must not make the mistake of over applying God's sovereignty to areas of our lives in such a way that limits God; we must avoid putting God in a box. More specifically, we have to avoid thinking, "God has to answer my prayer in such-and-such a way or he is not sovereign after all." That simply shows ignorance on our part.
God is fully sovereign. He will act according to his perfect character, will, and goodness. When he responds to our prayers in ways we do not like, let's not fall into hopelessness. God has not abandoned us. Rather, he is helping our sanctification process.
God's sovereignty is a reason for great hope. Let's avoid defining and comprehending that sovereignty in ways that God has not.