This is a great question. Let me begin with what fair trade is and then give a few thoughts.
Fair trade is a social movement that seeks to pay a fair amount of money for goods and services usually from third world countries to promote equality and economic justice. As one can see, the idea behind this movement is very noble. But whether it will persist is another question.
In my opinion, it will not thrive for two reasons.
First, the world economy is not doing well. For this reason, people are trying to cut costs where they can get them. So, if a developed nation could get away with paying less, they will. Moreover, the people will feel the same as they are feeling the economy pinch.
Second, within this context of economic hardships, there will always be people who will be willing to work for less. In short, fair trade will only thrive when the economy is doing well.