I've thought talk of the EU breaking up to be too unrealistic, but no one can deny the EU is in trouble. Why do countries keep joining it?
Look at the countries that wish to join (Croatia, Serbia, Albania) and the countries that have in recent years backed away from membership talks (Switzerland, Norway) and you've got your answer. The EU still offers a lot of incentives for the smaller and poorer countries of EEurope thanks to the cohesion funds + it's still seen as a sign of progress to be inside of the EU in these places.