No actual sovereign state has ever left the European Union. In fact, no state has even had its people vote on such a course of action. Therefore, we cannot know for certain what circumstances might cause a state to leave the EU. However, we can speculate on such circumstances.
The biggest problem that many states tend to have with the EU is that it, in their eyes, reduces their sovereignty. They feel that the EU has too much power over them. Therefore, this is the factor that is most likely to cause a state to leave the EU.
There are at least two ways in which this could conceivably happen. One of them has to do with financial control. For example, some Greeks have talked of leaving the EU because they do not like the degree to which it is attempting to force them to cut their governmental spending. The second has to do with regulations. There are many people (such as those in the UK) who do not like the rules that the EU imposes. They might not like, for example, laws that require the free movement of people between countries of the EU.
It is possible, then, that a country would want to leave the EU because it feels that the EU’s government has too much control and is forcing it to do things it would not like to do.